FINDING THE nth TERM IN A SEQUENCE

Formula's for the nth term

ALGEBRA

Here I intend to look at what is known as the nth term sequence. In doing so we will look at some examples and find the nth term which is known in mathematical terms by a "u" followed by a subscript(small) "n".

So what exactly is the connection( the pattern) between the "n" and the "un".

If we take a closer look at the un we can see that it goes up in two's (2's).

(Position) U         1    2    3    4    5

 ( Term)    Un          3    5    7    9   11

      n x 2               2    4    6    8   10

 

3 + 2 =   5

5 + 2 =   7

7 + 2 =   9

9 + 2 = 11

 

Therefore we can write down that un = 2n, in other words we are doubling the number.

Looking again we may need to adjust that 2n slightly;

2n means 2 x n therefore,

2 x 1 =   2

2 x 2 =   4

2 x 3 =   6

2 x 4 =   8

2 x 5 = 10

These are the numbers we have got after multiplyingn x 2, you will have noticed that they are 1 less in each case than the numbers in the unbracket, therefore we need to add on 1 in the formula.

Our formula now looks like this un = 2n + 1 (where the un is the nth term)

2 x n =   ? + 1 =  un

2 x 1 =   2 + 1 =   3

2 x 2 =   4 + 1 =   5

2 x 3 =   6 + 1 =   7

2 x 4 =   8 + 1 =   9

2 x 5 = 10 + 1 = 11

Answer:- un = 2n + 1

 

This is the type of question for the nth term, could be asked in an exam paper;

Find the nth term for the sequence; 2, 6, 10, 14, 18 ... (etc)?

To begin with we need to change this sequence into a table!

The "n" is the position and the “un” is the term.

The position simply represents the number of digits in a sequence, in the above there are "5" [ 2(which is 1), 6(which is 2), 10(which is 3), 14(which is 4), 18( finally this is number 5 )]

(Position) U          1    2     3     4     5

  ( Term)   Un            2    6   10   14   18

     n x 4                 4    8   12   16   20

So what exactly is the connection (the pattern ) between the "n" and the "un", in this question?

If we take a closer look at the "un" we can see that it is going up in four's (4's).

  2 + 4 =   6

  6 + 4 = 10

10 + 4 = 14

14 + 4 = 18

Therefore we can write down that un = 4n (which means 4 x n)

4 x 1 =   4

4 x 2 =   8

4 x 3 = 12

4 x 4 = 16

4 x 5 = 20

These are the numbers we have got after multiplying n x 4, you will have noticed that there are 2 more in each case than the numbers in the un term, therefore we need to subtract 2 in the formula.

Our formula now looks like this; un = 4n - 2 (where the unis the nth term)

4 x n =   ? - 2 = un

4 x 1 =   4 – 2 =  2

4 x 2 =   8 – 2 =  6

4 x 3 = 12– 2 = 10

4 x 4 = 16– 2 = 14

4 x 5 = 20– 2 = 18

Answer:- un = 4n - 2

 

In this example we need to find the nth term for this sequence;

Find the nth term for the sequence; 3, 6, 11, 18, 27 ... (etc)?

To begin with we need to change this sequence into a table!

This example is quite similar to the one above!!!!

LOOK CAREFULLY:-

The "n" is the position and the “un“ is the term

Again there are five numbers and they are holding the first five POSITIONS

The position simply represents the number of digits in a sequence, in the above there are "5" [ 3(which is 1), 6(which is 2), 11(which is 3), 18(which is 4), 27( finally this is number 5 )]

(Position) U           1    2     3     4    5

  ( Term)   Un             3    6   11   18   27

n2=(n x n)              1    4     9   16   25

So what exactly is the connection (the pattern ) between the "n" and the "un", in this question?

Is there a set pattern?

Are they going up in 2's or 4's? --- NO they are not!

  3 + 3 =   6

  6 + 5 = 11

11 + 7 = 18

18 + 9 = 27

In a case like this we would square (n2) the numbers and see what that brings us too.

Therefore we can write down that un = n2 (which means n x n)

1 x 1 =   1

2 x 2 =   4

3 x 3 =   9

4 x 4 = 16

5 x 5 = 25

These are the numbers we have got after multiplying n x n, you will have noticed that they are 2 less in each case than the numbers in the un term, therefore we need to add 2 in the formula.

Our formula now looks like this; un = n2 + 2 ( where the un is the nth term)

n x n =  ? + 2 = un

1 x 1 =   1 + 2 =   3

2 x 2 =   4 + 2 =   6

3 x 3 =   9 + 2 = 11

4 x 4 = 16 + 2 = 18

5 x 5 = 25 + 2 = 27

Answer:- un = n2 + 2

 

Another favourite question in exams is as follows;

The nth term of a sequence is represented by this formula:- un = 3n + 2

We are asked to;

(i) Find the first 4 terms

(ii) To find the 49th term

( i ) Find the first 4 terms

Our formula is:- 3n + 2 = un

Therefore our 1st term is u1 = 3 x 1 = 3 + 2 =   5

                             2nd term u2 = 3 x 2 = 6 + 2 =   8

                             3rd term u3 = 3 x 3 = 9 + 2 =  11

                            4th term u4 = 3 x 4 = 12 + 2 = 14

Our first four terms are; u1 , u2 , u3 , and u4

They end up as 5, 8, 11, and 14

 

\ First 4 terms are: 5, 8, 11, 14. (Answer:-)

 

 

( ii ) We have been asked to find the 49th term.

49th term: This will be known as u49

As before in part ( i ) the formula is; un = 3n + 2

Therefore we will replace the “n” with the 49

 u=       3n             + 2

u49 = (3 x 49) = 147 + 2 = 149

(Answer) u49 = 149

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Comments 258 comments

Bubble 7 years ago

what would be the nth term for 3,4,6,9...?


empeen 7 years ago

Really good one,very neatly explained with relevent examples

Same way you can postAP.,g.P. and H.P. also. I like it.


megan 7 years ago

what's the first five sequences of this nth term, 3n + 4?


tish. 7 years ago

7, 10, 13, 16, 19 :)


Oli 7 years ago

What about the nth term for 1,2,4,8,15,26,42... It goes up in 1,2,4,7,11,16 and that goes up in 1,2,3,4,5 please post back quickly, all I can work out is how to find what it goes up in innitially the formulae for that is as follows: Xn= n(n-1)/2+1 can't find how to make the actual original sequence.


amber 7 years ago

what is nth term for squared numbers


dana 7 years ago

whaat is the nth term of 4 6 8 10


,.jnmkl.jh 6 years ago

What is the nth term of this sequnce 5 10 15 20 25


ronak 6 years ago

what will be the nth term for 1, 12, 24, 36, 48


eivlys 6 years ago

how about this one. find the 9th term

n2/n+1


Raz 6 years ago

find a formula for 95, 90, 85,80

interms of n


dog 6 years ago

gd website


Irshad 6 years ago

what will be the nth term in this sequence

2,3,6,7,10,11......


Jk 6 years ago

Help!!!

What is the nth term in the sequence 107,68,29,-10,-49???pease help

me!!!


bbSTAR 6 years ago

tn=a(r^(n-1))

where:

tn = general term

a = first term

r = common ratio

n = position of the term


shwetha 6 years ago

if Tn=5-3n then find Tn+1 and Tn+2


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

whats the first five sequences of this nth term, 3n + 4?

Megan Please use the following;

3n + 4

3 x 1 = 3 + 4 = 7

3 x 2 = 6 + 4 = 10

3 x 3 = 9 + 4 = 13

3 x 4 = 12 + 4 = 16

3 x 5 = 15 + 4 = 19


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Thankyou Empeen just trying to help.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Shweta,

if Tn=5-3n then find Tn+1 and Tn+2

Tn=5-3n

then T(n + 1) = 5 - 3(n + 1)

= 5 - 3n - 3

= -3n + 2

So Tn + 1 = -3n + 2 (Ans)

And Tn +2 = 5 - 3(n + 2)

= 5 - 3n - 6

= - 3n - 1

So Tn + 2 = - 3n - 1 (Ans)


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

JK,

What is the nth term in the sequence 107,68,29,-10,-49?

Tn = a + (n - 1) d

a = 107

d = 68 - 107 = -39

Tn = 107 + (n - 1) x -39

...= 107 - 39n + 39

...= 146 - 39n (Ans)


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Ronak,

what will be the nth term for 1, 12, 24, 36, 48

a = 1

d = 12

Tn = 1 + (n - 1) x 12

....= 1 + 12n - 12

....= 12n - 11

......12n - 11 is the nth term


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t.elia 6 years ago from Northern Ireland Author

Eivlys

find the 9th term n2/n+1

Tn = n2 / n + 1

....= 9squared / 9 + 1

....= 81 / 10

....= 8.1 (Ans)


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t.elia 6 years ago from Northern Ireland Author

Raz,

find a formula for 95, 90, 85,80 in terms of n

Tn = a + (n - 1) x d

..a = 95

..d = 90 - 95 = -5

Tn = 95 + (n - 1) x -5

....= 95 - 5n + 5

....= 100 - 5n (Ans)


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

,.jnmkl.jh

(Position) U 1 2 3 4 5

( Term) Un 5 10 15 20 25

..n x 5

Therefore we can write down that un = 5n

U1 = 5 = 5 x 1

U2 = 10 = 5 x 2

U3 = 15 = 5 x 3

U4 = 20 = 5 x 4

U5 = 25 = 5 x 5

un = n x 5 = 5n

(Ans) un = 5n


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

dana,

(Position) U 1 2 3 4

( Term) Un 4 6 8 10

n x 2

4 + 2 = 6

6 + 2 = 8

8 + 2 = 10

Therefore we can write down that un = 2n

Looking again we may need to adjust that 2n slightly;

2 x 1 = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

These are the numbers we have got after multiplying n x 2, you will have noticed that they are 2 less in each case than the numbers in the un bracket, therefore we need to add on 2 in the formula.

Our formula now looks like this un = 2n + 2 (where the un is the nth term)

2 x n = ? + 1 = un

2 x 1 = 2 + 2 = 4

2 x 2 = 4 + 2 = 6

2 x 3 = 6 + 2 = 8

2 x 4 = 8 + 2 = 10

Answer:- un = 2n + 2


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Bubble,

U 1 2 3 4

Un 3 4 6 9

U1 = 3

U2 = 3 + (2-1) = 4

U3 = 4 + (3-1) = 6

U4 = 6 + (4-1) = 9

So Un = U(n-1) + (n-1)

Hope this helps


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Bubble,

U 1 2 3 4

Un 3 4 6 9

U1 = 3

U2 = 3 + (2-1) = 4

U3 = 4 + (3-1) = 6

U4 = 6 + (4-1) = 9

So Un = U(n-1) + (n-1)

Hope this helps


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

For further help follow the link in the hub "Let me solve your maths problems". Assistance can be found for

Bodmas

HCF

LCM

Prime and Composite numbers

Square Root

Cube Root

Place Values

Expanded Notation

Rounding off Numbers

Writing numbers as a product of their Prime Numbers


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Irshad,

This is just an ordinary sequence(not an arithematic one) The values go upwards in differences of 1's and 3's.

2 3 6 7 10 11

--- --- --- --- --- (Difference is)

1 3 1 3 1

so at some point in a sequence like this values would be ommitted and you would have to find them.


Ema 6 years ago

I really found this helpful. Please help me find the nth term of the sequence 1 , -2 , 3, -4,.... Thanks.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Ema,

In answer to your equation 1, -2, 3, -4;

This is not an arithematical sequence nor is it a geometric one, it is a general sequence that is alternating.

In this question "d" is not unique;

t2-t1 = -2 -1 = -3

t3-t2 = 3 -(-2) = 3 + 2 = 5

So the answer to this sequence is;

nth term is -n (if "n" is even)

............+n (if "n" is odd)

Hope this helps, thanks

Telia


Nico 6 years ago

please help,

i'm trying to work out the nth term for the following:

5 8 11 14

i know there's three difference between each number, but i'm getting confused as how to work this out...

thanks :)


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Nico,

(Position) U..1....2....3....4

( Term).......5....8....11...14

you are correct the common difference(d) is "3"

This tell you that your formula is going to start with "3n"

Therefore;

Go back to your table and put in your values in the 3n formula and see what else is required to solve it.

d x u

3 x 1 = 3 + ? = 5

3 x 2 = 6 + ? = 8

By now you'll see that you need to add on 2

So your formula is going to be 3n + 2


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

un = 3n + 2 (where the un is the nth term)


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Oli.

(i) 1, 2, 4, 8

Firstly we will put these values into a table

n 1 2 3 4

un 1 2 4 8

? ? ? (now to find the differences)

1 2 4 (The number is being doubled each time, this suggests that the rule

involves 2 to the power of something.)

un = ?

un = 2n

This time the formula involves subtraction of the power

Therefore; un = 2n - 1

21 - 1 = n0 = 20 which equals 1

22 - 1 = n1 = 21 which equals 2

23 - 1 = n2 = 22 which equals 4

24 - 1 = n3 = 23 which equals 8

if you check back to the above table the formula is correct

un = 2n - 1


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

That answer is 2 (to the power of n - 1)

Telia


Pien 6 years ago

can you find the rule for the nth term for the following sequence on numbers?

5,27,79,173

ive looked at it for a bit and i can only come up with this rule, which only works for the first 3 numbers:

6n^4/2n - n^n-1 +5


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Pien,

The rule you are looking for is

2n^3 + 3n^2 - (n - 1)

Hope this helps


waqas 6 years ago

let 1,3,2,5......find 6th term


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t.elia 6 years ago from Northern Ireland Author

The 6th term in this sequence is 7.

5th is 3


Krishnasingh 6 years ago

Some comments are not satisfactory. Also in many cases only nth term rule is given. how can we find the process?


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Krishnasingh

If you read through the above hub observing and understanding the tables you'll be able to follow the process to find the nth term.

Say your common difference is 4

then you are working with 4n plus or minus something to find the rest of your formula to solve the equation.

It takes a little bit of patience and practise.

If there is no visible difference then try squaring the numbers in the "u" bracket and find out what else you have to add or subtract to find the formula.

Please read over the worked examples again and you'll see not only is the nth term rule there but so is the process.

Good Luck


bubba #9 6 years ago

What is the ninth term in the following sequence? 6, 10, 14, 18, 22,...


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Bubba,

First start by finding the nth term.

Your difference is 4 so that tells you the formula is going to start as 4n + or - something.

So do out your table as shown in the worked examples above

...1...2...3...4...5

...6..10..14..18..22

4 x 1 = 4 + ? = 6 (? = 2)

4 x 2 = 8 + 2 = 10

4 x 3 = 12 + 2 = 14

So the formula is 4n + 2

Now use the formula to find the 9th term

U(9) = 4 x 9 = 36

36 + 2 = 38

Therefore 9th term = 38

Hope this helps.


rix 6 years ago

what is the nth sequence of 1,4,12,32,80


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Rix

Im not finding a common difference here have you wrote this question down properly? Please check


Georgia 6 years ago

What is the rule of this sequence? 23, 19, 13, 8


ema 6 years ago

what would be the nth term for the sequence 0,6,14,24,36,50

??????


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Georgia,

Your question doesn't follow any rule have you wrote it down properly?


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Ema,

tn = 6, 8, 10, 12, 14

a = 6

d = 2

tn = a + (n-1) 2

tn = a + 2n - 2


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

The nth term your looking for EMA is

tn = 2n + 4


Elias Jacobo 6 years ago

what is the next term of 1,6,4,9,7


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t.elia 6 years ago from Northern Ireland Author

Elias,

1..6..4..9..7..12..10


Jordan Newland 6 years ago

what is the first five terms for the nth term of 16-3n


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t.elia 6 years ago from Northern Ireland Author

Jordan,

16 - (3 x 1) = 13

16 - (3 x 2) = 10

16 - (3 x 3) = 7

16 - (3 x 4) = 4

16 - (3 x 5) = 1

So first five terms are as follows

13..10..7..4..1


ari h 6 years ago

two terms of an arithmetic sequence are a8=76 and a28=296 what's the rule for the nth term?


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi ari h,

an = a + (n - 1) d

now put in n = 8, an = 76

76 = a + (8 - 1) d

76 = a + 7d (equation 1)

an = a + (n - 1) d

now put n = 28, an = 296

296 + a + (28 - 1) d

296 = a + 27d ( equation 2)

Take the equations away from each other

296 = a + 27d

76 = a + 7d

--------------

220 = 20d

Then find common denominator and cancel down.

20d = 220

-----------

20 20 (CANCEL DOWN)

The two 20's cancel each other leaving "d" on its own on the left hand side of the equation.

On the right hand side of the equation 20 divides into 220 = 11

Therefore d = 11

a + 7d = 76

d = 11

a + 7 (11) = 76

a + 77 = 76

a = -1

Therefore a = -1, d = 11

Last Step in this Equation;

an = a + (n - 1) d

an = -1 + (n - 1) 11

an = -1 + 11n - 11

an = 11n - 12

So the nth term for a8 = 76 and a28 = 296 is;

an = 11n - 12

Hope this helps.


Humairaa Patel 6 years ago

This site is cool but it would be cooler if you added this place which says want to find out the nth term of something type it in here and you will get your answer


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Thanks Humaira Patel,

I will always answer irrespective of the fact that sometimes the question might not be asked in the correct hub. I am always glad when a student shows enough intution to ask a question if they are stuck or unsure of something.


Tom 6 years ago

Help please how is this worked out

first term 4 term to term rule x3 +1


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Tom,

un = 3x + 1

.....3 x 1 = 3 + 1 = 4

.....3 x 2 = 6 + 1 = 7

.....3 x 3 = 9 + 1 = 10 etc

Hope this helps


Varsha  6 years ago

I am stuck with this question. please help me out.

5A(n+1) + 1 = 5A(n) + n

Given A(5)=55. Find A(55)

I am using the brackets to denote that the numbers in the brackets are at the base. i.e A(n+1) denotes n+1 th term.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Varsha,

Using the brackets to denote that the numbers in the brackets are at the base.

5A(n + 1) + 1 = 5A(n) + n

Given A(5) = 55

.......A(55) = ?

5A(n + 1) + 1 = 5A(n) + n

Take the 1 over the = sign to the other side and it becomes -1 (change side ,change sign)

5A(n + 1) = 5A(n) + n - 1

Now divide each side by 5 to get A(n + 1) on its own;

Therefore

A(n + 1) = 5A(n)/5 + (n - 1 /5)

The 5's cancel each other out and your left with the formula;

A(n + 1) = A(n) + (n - 1 / 5)

So use this formula to solve A(55)

We know A(5) = 55

So we will find A(6)....up til A(55)

This will have to be done manually as the difference is 0.2 and it is compoundly added on to the next total. OK so far!

So lets take the Formula we found and start plugging in the values to solve this equation.

A(n + 1) = A(n) + (n - 1 / 5)

A(5) = 55

A(5 + 1) = A(5) + (5 - 1 / 5)

.........= A(5) + (4 / 5)

.........= 55 + 0.8 = 55.8

_________________________________________________________

A(6 + 1) = A(6) + (6 - 1 / 5)

.........= A(6) + (5 / 5)

.........= 55.8 + 1 = 56.8

_________________________________________________________

A(7 + 1) = A(7) + (7 - 1 / 5)

.........= A(7) + (6 / 5)

.........= 56.8 + 1.2 = 58

and so on until

A(54 + 1) = A(54) + (54 - 1 / 5)

.........= A(54) + (53 / 5)

.........= 329 + 10.6 = 339.6

At the start of this equation I was able to find the (n - 1 / 5) to be 10.6 but had to do the whole equation manually to find the 339.6 value.

Therefore A(55) = 339.6

Hope this helps


Varsha 6 years ago

Thank you for your quick response.

Sorry to bother you again ...but require one clarification...

Did you calculate every term to arrive to A(55)or you calculated it directly by some formula. i.e how you got A(54) as 329?


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Varsha,

Sorry but there is no Formula for this aspect of the equation - each term has to be calculated individually to arrive at A(55).

Is this a homework question?


Varsha 6 years ago

I am giving some entrance exam. This was one of the question in the mock test which has a time constraint. Anyways will have to skip such questions as they are too time consuming or will have to search some better method for solving this.

Thank you for your response.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Varsha,

If you practice this question you should be ok, but please don't skip it as this is one of the question which would separate the "men from the boys" so to speak. The first part of this question is relevantly straight forward- do that then come back to finish it, this will show them you know what you are doing. It seperates the "A" students from the "C" students. Good Luck


Varsha 6 years ago

Hi

Was trying for long to find some different method to solve this. Check this out....

Using {} these brackets to denote the actual brackets.

5A(n + 1) + 1 = 5A(n) + n

A(n+1) = A(n) + 1/5 {n-1}

A(6)= A(5)+ 1/5 {5-1}

....= 55 + 1/5 {4}

Similarly A(7) = A(6)+ 1/5{6-1}

.... = 55 + 1/5 {5} + 1/5 {4}

.... = 55 + 1/5 {4 + 5}

So A(55) = 55 + 1/5 {4+5+6+7......+52+53}

... = 55 + 1/5 {53x54/2 - {3+2+1}

... = 55 + 1/5 {1431 -6}

... = 55 + 285

... = 340

which is close to 339.6

What is your opinion? Is this a correct method?


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Varsha,

Sorry for the delay was out.

OK here goes , I made a slight mistake of 0.4 at the A(40) part of this equation for that I apologise. The answer should have been 202 at that point and not 201.6 as I had noted in my notepad.

As a result after plugging in your idea I have got this to work as per your answer,

A(n + 1) = A(n) + [n - 1 / 5] + d

...........A(55) + [4+5+6+7+8+9....+53 - 1 / 5] + d

...........A(55) = [1425 - 1 / 5] + 0.2

..................284.8 + 0.2 = 285

..................285 + 55 = 340

0.2 being the difference each time

Absolutely brilliant Varsha

Good Luck


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Although we come up with a formula Varsha you still need to work out the first 3 or 4 terms manually to see if there is any correlation within the problem.

My idea was to find the first term of the series and then using the Arithmatic progression formula to find the value of A(55) - for that the difference between two terms has to be constant - so we don’t have a choice here but to do it manually:(

If you work out a few more of them you will find you are always adding 55 at the end in the equation plus the difference of 0.2

Good Luck with the entrance exam.


Varsha 6 years ago

Ya dats true.. Will have to do that much of calculations...No other option :(

Anyways, Thanks a lot.

Sorry but will keep on bothering you till my exams.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Varsha,

Glad to be of a help to you and keep in contact - if you need anything else clarified before your exam don't hesitate to contact me.

Good Luck in your exam studies.


Sheena  6 years ago

what's is the nth term for 38, 33, 28, 23, 18

and 640, 320, 160, 80 I',m having a hard time with this thank you


varsha 6 years ago

Hi,

Had put this question in your trigonometric forum. But not got any reply yet.waiting for your response.

"Need i more help from you.

I tried searching sin theta table for multiples of 5 on internet which is in fractions. Like sin theta 75 degree, 80 degree etc in fractions. But the search showed sin theta table in decimals. Do you have one with fractions?

My purpose is to learn these fractions so as to answer area of triangle questions by the 1/2 ab sin theta formula, where a & b are the sides and theta is the angle between them.

Also are there any other trigonometric formulas for finding areas of geometric figures?"


ssss!! 6 years ago

please help me on this one pleaseeeeeeeeeeeeeeeeee.

i really need to know this today and right now b4 i go off..

what's the first 4 terms of the number sequence using the nth term rule which is: N3+3 ???

the first number 3 is actually supposed to be over the n and small...


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

SSSS,

Do you mean N cubed + 3

If so then,

1 x 1 x 1 = 1 + 3 = 4

2 x 2 x 2 = 8 + 3 = 11

3 x 3 x 3 = 27 + 3 = 30

4 x 4 x 4 = 64 + 3 = 67

Please clarify if this is correct


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Sheena,

tn = a + (n - 1) d

a = 38

d = -5

tn = 38 + (n - 1) -5

tn = 38 -5n + 5

tn = 43 - 5n (answer)

In the next one the sequence is

640,...320,...160,...80

1st term = 640

2nd term = 320 = 640 / 2 = 1st term / 2

3rd term = 160 = 320 / 2 = 2nd term / 2

4th term = 80 = 160 / 2 = 3rd term / 2

so we can say

nth term = n - 1 / 2

(n - 1)th term is previous to nth term


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Varsha,

When

theta is 0...sin theta is 0

theta is 30 degrees...sin theta is 1/2

theta is 45 degrees...sin theta is 1/squareroot 2

theta is 60 degrees...sin theta is squareroot 3 / 2

theta is 90 degrees...sin theta is 1

theta is 120 degrees...sin theta is sq root 3 / 2

theta is 135 degrees...sin theta is sq root 2 / 2

theta is 150 degrees...sin theta is 1 / 2

theta is 180 degrees...sin theta is 0

theta is 210 degrees...sin theta is -1 / sq root 2

theta is 225 degrees...sin theta is -sq root 2 / 2

theta is 240 degrees...sin theta -sq root 3 / 2

theta is 270 degrees...sin theta is -1

theta is 300 degrees...sin theta is - sq root 3 / 2

theta is 315 degrees...sin theta is - sq root 2 / 2

theta is 330 degrees...sin theta is -1 / 2

theta is 360 degrees...sin theta is 0

Hope this helps Varsha


varsha 6 years ago

Thanks a lot..


mike 6 years ago

does this sequence diverge or converge, and if it converges, what is the limit?

(2n+1)/(1-3sqrt(n))?? thanks


????????????? 6 years ago

wow !


sebastian 6 years ago

what is the nth term of the sequence 6,14,24,36? is it a quadratic?


michael 6 years ago

what is the general term of 1,2,7,11,16,22? thank you


michael 6 years ago

Is there any technique to get the general terms? plsss help me. huuuh. thank you.


andy 6 years ago

Here's a weird one we can't figure out:

0, 2, 4, 8, 24, 220

What's the next term and rule? I need to figure the first 12 terms. Pls answer to ahofer@nstsystems.com if possible.


michaelneLa 6 years ago

help me plsss.. our final exam is coming up.. can you help for the general term of this no. 3,3,6,6,9,9,12,12 thanks in advance


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Mike.

Sorry about the delay in answering your question but Ive been very busy. Now to get caught up!

This sequence diverges.

(2n + 1) / (1 - 3 sqrt n)

rationalise the denominator

(2n + 1) ( 1 + 3 sqrt n) / (1 - 3 sqrt n)(1 + 3 sqrt n)

= (2n + 1) (1 + 3 sqrt n) / 1 - 9n

= 2n + 2n.3 sqrt n + 1 + 3 sqrt n / 1 - 9n

= 2n + 6(n)to the power 3/2 + 1 + 3 sqrt n

Divide each term by the highest power of n

(e.g) (n to the power of 3/2)

= 2n / n to the power 3/2 + 6n to the power 3/2 / n to the power 3/2 + 1 / n to the power 3/2 + 3 sqrt n / n to the power of 3/2 all over 1 / n to the power 3/2 - 9n / n to the power of 3/2

= 2 / n to the power of 1/2 + 6 + 1 / n to the power of 3/2 + 3 / n squared, all over 1 / n to the power of 3/2 - 9 / n to the power 1/2

put the limit n arrow infinity (use sign for infinity which looks like an eight sideways)

= 2 / infinity + 6 + 1 / infinity + 3 / infinity all over 1 / infinity - 9 / infinity

= 0 + 6 + 0 + 0 / 0 - 0

= 6 / 0

= infinity

Therefore the limit of this sequence is infinity and clearly this is a diverging sequence.

Hope this helps and Good Luck.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Sebastian,

what is the nth term of the sequence 6,14,24,36? is it a quadratic? NO

6 = 6 x 1 = (6 + 1) x (1 + 1)

14 = 7 x 2 = (6 + 2) x ( 1 + 2)

24 = 8 x 3 = (6 + 3) x ( 1 + 3)

36 = 9 x 4

so nth term {6 + (n - 1)} x {1 + (n - 1)}

...........= (6 + n - 1) (1 + n - 1)

...........= (n + 5)(n)

...........= n squared + 5n

Hope this helps and good luck


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Michael,

what is the general term of 1,2,7,11,16,22?

The pattern is as follows;

1 + 0 = 1

1 + 1 = 2

2 + 2 = 4

4 + 3 = 7

7 + 4 = 11

11 + 5 = 16

16 + 6 = 22

22 + 7 = 29

So next term is 29 ( 8th term = 29)

9th term = 8th term + 8

..........29 + 8 = 37

Therefore the general term is;

Term (n + 1) = Term (n) + n

T (n + 1) = T (n) + n

Hope this helps, Good Luck

There is no magic formula for working out sequences except work out their pattern, tedious as it is.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi MichaelneLa,

can you help for the general term of this no. 3,3,6,6,9,9,12,12

Series questions are set out like this double 3's, double 6's etc so general term is 3n + 3, 3n + 3

3 x 1 = 3 + 3 = 6

3 x 2 = 6 + 3 = 9

3 x 3 = 9 + 3 = 12

Term you are looking is 3n + 3

Hope this helps and Good Luck


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi Caroll,

What's the nth term of 1, 1/2, 3, 1/4, 5, 1/6, 7, 1/8, 9, 1/10, 11

From the above sequence the 9th term is 9

The sequence is found out by the following method;

Every odd number increases by 2

First term = 1

Third term = 3 etc

Whereas 2 is being added to the demoninator each time to get the next even term.

nth term is;

= 1 + (n - 1) 2

= 1 + 2n - 2

= 2n - 1

Therefore 2n - 1 is the nth term for odd terms.

For the even terms 1/2, 1/4, 1/6, the nth term is 1/(2n)

that is written as a fraction 1 over 2n

Hope that helps and Good Luck


bob lee 5 years ago

nive post. really helped.


turkish 5 years ago

what is the nth term of 6, 8, 10, 12, 14, 16... ??

Please help meee :(


Jai 5 years ago

t.elia: Your solution (4 posts above mine) for "What's the nth term of 1, 1/2, 3, 1/4, 5, 1/6, 7, 1/8, 9, 1/10, 11" is incorrect. It should be n for odd numbers and 1/n for even.


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Dear Jai,

Im sorry you have made a BIG mistake in your calculations. Please re-check them, not for my sake but for your own educational purposes.The answer you posted above is WRONG!

My Calculations are CORRECT

The answer for the workings of the nth term of this equation are as I stated;

Therefore 2n - 1 is the nth term for odd terms.

For the even terms 1/2, 1/4, 1/6, the nth term is 1/(2n)

that is written as a fraction 1 over 2n

Many Thanks for the post

Telia


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi Turkish,

The nth term you are looking for to solve this equation is;

2n + 4

Regards

Telia


Iltbbas 5 years ago

What the nth term for 15,21,27,33,39

and 19,13,7,1,-5


hi! I need help!  5 years ago

rule of 14,23,32,41,50? and ule of 1,6,11,16,21 please1

thanks!


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi lltbbas,

Tn = a + (n-1) d

a = 15

d = 21 - 15 = 6

Tn = 15 + (n-1) x 6

Tn = 15 + 6n - 6

Tn = 9 + 6n (ANS)

Now for the second one;

Tn = a + (n-1) d

a = 19

d = 13 - 19 = -6

Tn = 19 + (n-1) x -6

Tn = 19 - 6n + 6

Tn = 25 - 6n (ANS)

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi ,

Here is the help you requested

Tn = a + (n-1) d

a = 14

d = 23 - 14 = 9

Tn = 14 + (n-1) x 9

Tn + 14 + 9n - 9

Tn = 5 + 9n (ANS)

The next one is;

Tn = a + (n-1) d

a = 1

d = 6 - 1 = 5

Tn = 1 + (n-1) x 5

Tn = 1 + 5n - 5

Tn = -4 + 5n (ANS)

Good Luck and hope this helps.


Abhie 5 years ago

What is the 10th term of the Tn = n (n + 5)?


lui 5 years ago

please help find the next three sequence

20,4,16,37


ahmed 5 years ago

superb.................found it really helpful....


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Dear Hafsa,

I never judge a book by its cover.

Telia


iamhappy 5 years ago

whta i the the nth term formula for 3,6,9,12,15,18 ......Please!!


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Dear iamhappy,

Your common difference is 3, therefore this tells you to write down 3n

Now if you work it out using the layout of the tables at the start of this hub you will find the following;

3 x 1 = 3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12

so therefore your answer is 3n

Good luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi chipcat,

3n + 4 what is the 8th term of this question?

3n = ( 3 x n)replace the "n" with the "8"

Therefore;

3 x n

3 x 8 = 24 + 4 = 28

So 8th term of this question is 28


Daisy 5 years ago

What would the nth term of the sequence 1,13,37,73,... be? Can someone please explain with steps. Thank you!


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi Daisy,

You need to follow this method to complete this math;

1, 13, 37,73.....

The general form of this sequence is;

an^2 + bn + c (^2 means squared)STEP 1 of this equation

Constant = 13 - 1 = 12

a = constant/2 (constant divided by 2) = 12 / 2 = 6

a = 6

Plug a = 6 into STEP 1

an^2 + bn + c (^2 means squared)STEP 1

6n^2 + bn + c (STEP 2 of this equation)

for n = 1

Next

6(1) + b(1) + c = 1

6 + b + c = 1

b + c = -5 (STEP 3 of this equation)

Now n = 2 in STEP 2

6(2)^2 + b(2) + c = 13

2 x 2 = 4 x 6 = 24

24 + 2b + c = 13

2b + c = -11 ( STEP 4)

STEP 3 = b + c = -5

STEP 4 = 2b + c = -11

(-) (-)

------------------------

= -b/-1 = 6/-1

Cancel down b= -6

Plug 6 = -6 (in @ STEP 3)

b + c = -5

-6 + c = -5

c = -5 + 6

c = 1

Plug a = 6, b = -6, & c = 1 (into STEP 1

an^2 + bn + c

Your Answer becomes

6n^2 - 6n + 1 ( Answer)

Good Luck...Hope this helps.


Daisy 5 years ago

Hey! Thank you so much :) That helped a lot, its so clearly explained! Thanks again!


hellp 5 years ago

find the a8 for the sequence a1=-2, an=3a(n-1) +6


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi hellp...

Given:-

a(1) = -2

an = 3a(1) (n - 1) + 6

Solution:-

an = 3a (n - 1) + 6

Plug n = 8 and a(1) = -2

a(8) = 3(-2) (8 - 1) + 6

a(8) = -6 (7) +6

a(8) = -6 x 7 + 6

a(8) = -42 + 6

a(8) = -36

Hope this helps & Good Luck


Ash 5 years ago

find the nth term for 1/5, 2/6, 3/7, 4/8, 5/9... ?

I can see the pattern but I'm not sure how to express it Help? :)


brookie 5 years ago

position: 1 2 3 4 5 6

value of : 5 14 23 32 ??

term


killah 5 years ago

really helpful


5 years ago

help me to solve this:

(28% - 8%) / 1.4 = ?


R.Purnalingam 5 years ago

What is the nth term of the sequence 0,1,1,2,2,3,3,4,4,5,5......?


Nikee 5 years ago

The nth term of a sequence is 100-2n

What is the 1st term, 15th term and 30th term?


megan 5 years ago

hi what is the sequence and the result in nth term for these numbers please, 23, 16, 9, 2

Thanks


megan 5 years ago

hi again i posted a minute ago also can you tell me what the rule is as well as the sequence and the result in nth term

thanks


amar 5 years ago

whats the nth term of 4,8,16


Bitsy 5 years ago

I am looking at this pattern: 7,0,0,0...I need to find the next 2 numbers in the pattern and I can't even see the rule for the pattern. Can anyone help?


Arpita 5 years ago

how do i get the first five numbers in the sequence when 34-5n is the nth term rule?


trung 5 years ago

what is the nth term of pattern 20,44,76,116....

i know it is adding multiples of 8 each time


Rohit 5 years ago

What is the formula for 1,2,3,4,5,6

11,9,7,5,3,1


exam 5 years ago

I have an exam tommorow. Can you plz tell me the formula for: 20, 17, 14, 11, 8,


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

EXAM,

The formula you need to use to solve this equation is as follows;

Tn = a + (n - 1) d

Therefore

a = 20

d = 17

Take d away from a

17 - 20 = -3

Now plug the results into your formula;

Tn = a + (n - 1) d

...= 20 +(n - 1) -3 (multiply out the brackets)

...= 20 -3n + 3

...= 23 - 3n

This is your answer!!

Good Luck in your Exams tomorrow.


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Arpita,

How to find the first 5 numbers in the sequence 34 - 5n

-5 x n

-5 x 1 = -5

.......= -5 + 34 = 29

-5 x 2 = -10

.......= -10 + 34 = 24

-5 x 3 = -15

.......= -15 + 34 = 19

-5 x 4 = -20

.......= -20 + 34 = 14

-5 x 5 = -25

.......= -25 + 34 = 9

So therefore the first 5 numbers in the sequence are ;

29 , 24 , 19 , 14 , 9

Good Luck hope you understand this.


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

MEGAN

The formula you need to use is;

Tn = a + (n - 1) d

a = 23

d = 16

16 - 23 = -7

Now plug the results into your formula;

Tn = 23 + (n - 1) d

Tn = 23 + (n - 1) -7 (multiply out the brackets)

...= 23 -7n + 7

...= 30 - 7n (nth term rule)

Therefore;

-7 x 1 = -7

.......= -7 + 30 = 23

-7 x 2 = -14

.......= -14 + 30 = 16

-7 x 3 = -21

.......= -21 + 30 = 9

-7 x 4 = -28

.......= -28 + 30 = 2

-7 x 5 = -35

.......= -35 + 30 = -5 etc

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

BROOKIE

Use the following formula;

Tn = a + (n - 1) d

a = 5

d = 14

14 - 5 = 9

Therefore plug the results into the formula as follows;

Tn = a + (n - 1) d

...= 5 + (n - 1) 9 (multiply out the brackets)

...= 5 + 9n - 9

...= -4 + 9n (This is your nth term rule)(ANSWER)

9 x (1) = 9 - 4 = 5

9 x (2) = 18 - 4 = 14

9 x (3) = 27 - 4 = 23

9 x (4) = 36 - 4 = 32

9 x (5) = 45 - 4 = 41 etc

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

NIKEE

The nth term of a sequence is 100-2n

What is the 1st term, 15th term and 30th term?

100-2n

First Term

2 x (1) = 2

100 - 2 = 98

Fifteenth Term

2 x (15) = 30

100 - 30 = 70

Thirtith Term

2 x (30) = 60

100 - 60 = 40

1st Term = 98

15th Term = 70

30th Term = 40

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

ROHIT

You need to follow this formula for the numbers 11,9,7,5,3,1

Tn = a + (n - 1) d

a = 11

d = 9

9 - 11 = -2

Tn = a + (n - 1) d

Tn = 11 + (n - 1) -2 (multiply out brackets)

Tn = 11 -2n = 2

...= 13 - 2n (ANSWER)( nth term rule)

Good Luck


Bob 5 years ago

what are the next 5 nth terms for 4n+4?!?!?!?!!?!?

thanks.


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

BOB

The next 5 terms for the nth term rule 4n + n are;

4 x (n) + 4

Term 1

4 x (1) = 4 + 4 = 8

Term 2

4 x (2) = 8 + 4 = 12

Term 3

4 x (3) = 12 + 4 = 16

Term 4

4 x (4) = 16 + 4 = 20

Term 5

4 x (5) = 20 + 4 = 24

Hope this helps


quadlet 5 years ago

what would be the next 3 terms for o.25n+5 and the 10th term


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

QUADLET

I take it this is 0.25n + 5

Workings of First Term;

0.25n + 5

= 0.25 x (n) + 5

0.25 x (1) = 0.25 + 5 = 5.25 ( Ans)

Workings of Second Term;

0.25 x (2) = 0.50 + 5 = 5.5 ( Ans)

Workings of Third Term;

0.25 x (3) = 0.75 + 5 = 5.75 ( Ans)

Workings of Tenth Term;

0.25 x (10) = 2.5 = 5 = 7.5 ( Ans)

Good Luck


sophie 5 years ago

what will be the nth term for 95,90,85,80,75 ? please help, really appreciated :)


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

SOPHIE

For the sequence 95,90,85,80...

The formula you need to use is as follows;

Tn = a + (n - 1) d

a = 95

d = 90

90 - 95 = -5

Now plug this into your formula;

Tn = a + (n - 1) d

Tn = 95 + (n - 1) -5 (multiply out the brackets)

Tn = 95 -5n + 5

Tn = 100 - 5n ( Answer)

Prove answer:-

100 - 5n ( This means 5 multiplied by n)

100 - 5 x 1

100 - 5 = 95

Next

100 - 5n

100 - 5 x 2

100 - 10 = 90

etc

Good Luck


James 5 years ago

Hi please can you tell me the nth term for

36 42 48 54 60

-8 -3 2 7 12

1.2 1.4 1.6 1.8 2


sam 5 years ago

how do you do like 5/12 = n/6


Bill 5 years ago

Hi please can you tell me the nth term for

36 42 48 54 60

-8 -3 2 7 12

1.2 1.4 1.6 1.8 2


dell336 5 years ago

Please can you tell me the sequence pattern for 3 15 35 63


Emma 5 years ago

Can you please tell me the sequence pattern for 2, 8, 14, 20 AND 8, 5, 2, -1 please??

Also can you give the answer for tomorrow (26 September)?


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

SAM

5/12 = n/6

You will need to cross multiply here

That will give you;

12n = 30

..n = 30/12 (Cancel Down by dividing by 6)

..n = 5/2

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

P

( 28% - 8%)/ 1.4

= (20%)/ 1.4

= 20 over 100/ 1.4

= 0.2/ 1.4

= 1/7 (Ans)


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

EMMA

the sequence pattern for 2, 8, 14, 20

Use the following formula;

Tn = a + (n - 1 ) d

a = 2

d = 8

8 - 2 = 6

Tn = a + (n - 1) d

...= 2 + (n - 1 )6

...= 2 + 6n - 6

...= 6n - 4 (Ans)

Prove your Answer;

6n - 4

6(1) - 4 = 6 - 4 = 2

6(2) - 4 = 12 - 4 = 8

6(3) - 4 = 18 - 4 = 14

6(4) - 4 = 24 - 4 = 20

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

EMMA

the sequence pattern for 8, 5, 2, -1

Use the following formula;

Tn = a + (n - 1 ) d

a = 8

d = 5

5 - 8 = -3

Tn = a + (n - 1 ) d

Tn = 8 + (n -1) -3

...= 8 - 3n + 3

...= -3n + 11 (Ans)

Prove your Answer;

-3n + 11

-3(1) + 11 = -3 + 11 = 8

-3(2) + 11 = -6 + 11 = 5

-3(3) + 11 = -9 + 11 = 2

-3(4) + 11 = -12 + 11 = -1

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

BILL

the nth term for 36,42,48,54,60

Use the following formula;

Tn = a + (n - 1 ) d

a = 36

d = 42

42 - 36 = 6

Tn = a + (n - 1 ) d

...= 36 + (n - 1) 6

...= 36 + 6n - 6

...= 30 + 6n (Ans)

Prove your Answer;

30 + 6n

6(1) + 30 = 6 + 30 = 36

6(2) + 30 = 12 + 30 = 42

6(3) + 30 = 18 + 30 + 48

6(4) + 30 = 24 + 30 = 54

6(5) + 30 = 30 + 30 = 60

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

BILL

the nth term for -8 -3 2 7 12

Use the following formula;

Tn = a + (n - 1 ) d

a = -8

d = -3

-3 - (-8) = 5

Tn = a + (n - 1 ) d

...= -8 + (n - 1) 5

...= -8 + 5n -5

...= -13 + 5n

Prove your Answer;

-13 + 5n

5(1) - 13 = 5 - 13 = -8

5(2) - 13 = 10 - 13 = -3

5(3) - 13 = 15 - 13 = 2

5(4) - 13 = 20 - 13 = 7

5(5) - 13 = 25 - 13 = 12

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

BILL

the nth term for 1.2,1.4,1.6,1.8,2

Use the following formula;

Tn = a + (n - 1 ) d

a = 1.2

d = 1.4

1.4 - 1.2 = 0.2

Tn = a + (n - 1 ) d

...= 1.2 + (n -1) 0.2

...= 1.2 + 0.2n - 0.2

...= 1 + 0.2n (Ans)

Prove your Answer;

1 + 0.2n

0.2(1) + 1 = 0.2 + 1 = 1.2

0.2(2) + 1 = 0.4 + 1 = 1.4

0.2(3) + 1 = 0.6 + 1 = 1.6

0.2(4) + 1 = 0.8 + 1 = 1.8

0.2(5) + 1 = 1.0 + 1 = 2.0 = 2

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

DELL336

the sequence pattern for 3 15 35 63

Sum of n terms = n/2 (2a + (n - 1) d )

Tn = 3 + 12 + 20 + 28... (add following term to get next number in sequence)

Tn = 3 + (n - 1/ 2) (2(12) + (n - 2) 8)

Tn = 3 + (n - 1/ 2) 24 + 8n -16

Tn = 3 + (n - 1/ 2) + 8n + 8

Tn = 3 + 8(n - 1 )(n + 1)/ 2

Tn = 3 + 4(n^2 - 1)

Tn = 3 + 4n^2 -4

Tn = 4n^2 - 1 (Ans)

PROVE YOUR aNSWER;

4n^2 - 1

4(1^2) - 1 = 4 - 1 + 3

4(2^2) - 1 = 16 - 1 = 15

4(3^2) - 1 = 36 - 1 = 35...

Good Luck


Michelle 5 years ago

Please could u help me find the nth term for:

Q 1, 1/2, 1/8, 1/4, .....

this is the only part of the sequence i have sorry .


George 5 years ago

nth term formula for 8, 19, 34, 53, 76, 103


need help 5 years ago

what is the formula of the sequence 10,8,5,1


Oliver 5 years ago

What is are the next three terms for this sequence: 1,2,2,4,8

Im really confused!


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

MICHELLE,

The nth term for 1, 1/2, 1/4, 1/8...

1/2^0 = 1

1/2^1 = 1/2

1/2^2 = 1/4

1/2^3 = 1/8

1/2^4 = 1/16

Therefore;-

tn = 1/2^n-1

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

GEORGE,

nth term formula for 8, 19, 34, 53, 76, 103

The difference is 4 at the second level, letting you know you are dealing with a squared number in the answer.

tn = 2^n2 + 5n + 1 (Answer)

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

NEED HELP,

what is the formula of the sequence 10,8,5,1

Yn = X - n

yn = final term

n = number of terms

X = initial term

Explanation with Example

n = 2, X = 10

yn = x - n

....10 - 2 = 8

Yn = X - n (Answer)

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

OLIVER,

What is are the next three terms for this sequence: 1,2,2,4,8

1 x 2 = 2

2 x 2 = 4

2 x 4 = 8

1st term x 2nd term = Next term

4 x 8 = 32

8 x 32 = 8192

32 x 8192 = 262,2144

So Answer is 32,8192,2622144

Good Luck


saf 5 years ago

ok i know this is random but if you start with 2 and double each time then what is the number if the nth term is n+3

then 105-5n

2n-0.5v

thanx


renee 5 years ago

what are the first 5 nth term of 3n+6


Bex 5 years ago

What's the nth term for: -1 +1 -1 +1 -1.

Doing my GCSEs and stuck on homework.


Russ 5 years ago

Can somebody help me with the sequence of 1 8 9 12 please...are there 2 sequences? What follows after 12? Much appreciated!


Me 5 years ago

WHAT IS THE FORMULA FOR tHIS SEQUENCE PLEAAAASE! 1 8 9 12


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

RUSS & ME,

Here is help with the sequence for your formula;

1 , 8 , 9 , 12

1^2, 2^3, 3^2 , (2*3*2) = 12

So the first number is squared = 1

...the second number is cubed = 8

...the third number is squared = 9

...the fourth is the powers multiplied (2*3*2) = 12

The fifth number will be 5^2 = 25

The sixth number will be 6^3 = 216

The seventh number is 7^2 = 49

The eighth will be the powers multiplied (2*3*2) = 12

and so on ......

Hope this helps

Good Luck


dom 5 years ago

3,8,15,24,35 what is the rule for that? im stuck !


David 5 years ago

Excuse me, would you help me with 50,48,46,44 and 3,8,15,24,35 and 53,56,61,68 please, thanks.


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

DOM & DAVID,

you have both asked for the same problem here;

3, 8, 15, 24, 35

First difference is 5, 7, 9, 11

Second difference is 2

The Sum of the n terms is written as Sn and we know that the nth term = Tn = Sn - (Sn-1)

Tn = a + (n - 1) d

Tn = n/2 [ 2a + (n - 1) d ]

Tn = n/2 [ 2*3 + (n - 1) 2]

Tn = n/2 x 6 + n/2 x (n - 1)2 (cancel down)

Tn = 3n + n^2 - n

Tn = n^2 + 2n (Answer)

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

DAVID

50, 48, 46, 44

Tn = a + (n - 1) d

a = 50

d = 48

48 - 50 = -2

Tn = a + (n - 1) d

Tn = 50 + (n - 1) -2

Tn = 50 - 2n + 2

Tn = 52 - 2n (Answer)

Good Luck


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

DAVID

53, 56, 61, 68

first difference is 3, 5, 7

second difference is 2

Tn = a + (n - 1) d

The Sum of the n terms is written as Sn and we know that the nth term = Tn = Sn - (Sn-1)

Tn = 53 + 3 + 5 + 7

Tn = 53 + n/2[ 2*3 + (n - 1) 2]

Tn = 53 + n/2 x 6 + 2(n - 1) (Cancel down)

Tn = 53 + 3n + n^2 - n

Tn = n^2 + 2n + 53 (Answer)

Good Luck


Mahmoud Shahoud 5 years ago

Hi , You're smart , but all comments don't help me .

can you help me .

I have this sequence .

1 1 1 1 1 1 1 1 1 2

I want to calculate the 11st element and 12nd element

I want Math Equations .

I have a product gave me the answer but I want the way .

11st term = 11

12nd term = 56

please help me .


liv 5 years ago

26-4n?


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

LIV

26-4n

26 - 4 x N

26 - 4 x (1) = 22

26 - 4 x (2) = 18

26 - 4 x (3) = 14 etc

Hope this helps

Good Luck


bubble 543 5 years ago

what would the answer be for the nth term for a sequence is n-2/ n squared

write the first three terms of the sequence


oscar 5 years ago

can you solv please 7,10,13,16


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Oscar,

Answer is 3n + 4

3 x 1 = 3 + 4 = 7

3 x 2 = 6 + 4 = 10

3 x 3 = 9 + 4 = 13 etc

Good Luck & hope this helps


shreyansh 5 years ago

The value of (2/3)(3/4)(4/5).....(1-1/n)=


Jamie 5 years ago

Hi, can you help me.

If i have these 4 numbers, 12 15 18 21, what's the sequente to get the nth term?


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

Hi Jamie

Your answer is 3n + 9


Paul 4 years ago

My homework sheet says that i have to write a rule in terms of n, i don't know what that means, the website for my homework is http://docs.google.com/viewer?a=v&q=cache:ap2taSTK.../maths/docs/building_number_patterns.doc+building+investigative+skills&hl=en&gl=uk&pid=bl&srcid=ADGEESgdc2qKUJbnfZK9K6L22BqBGd27GIaVEhDj6m_QE5xBedMtgqj5QD7hfd1vx0armiQYpFn4mPs83vidpckpAmTdbMgP_2PR7u30s46xICSkUbnCcSq1TaTrXxr-ywh0FKdy2oaH&sig=AHIEtbScDxgftte_31i6WwekjrGnqCDRgA, i also don't get question 4


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

Hi Paul, this link you provided isn't working.


student 4 years ago

hello plaese help me find Recurrence Relations

t(n)=t(3n/5)+t(2n/5)+n


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

Ogleoo,

48 - 4n

48 - (4 x 1)= 48 - 4 = 44

48 - (4 x 2)= 48 - 8 = 40

48 - (4 x 3)= 48 - 12 = 36 etc

I hope you find this easy to follow

Good Luck


ogleoo 4 years ago

thank you so much


ogleoo 4 years ago

i keep forgetting that n means term number!!!


MAHI 4 years ago

WHAT IS AP?


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

MAHI,

Arithematic Progression:-

A sequence of numbers. Let's start with a number: a1.

Now add a number d, (for "difference").

We get a1 + d and the first 2 terms in our sequence are:

a1, a1 + d

For the next term, let's add d to that last term and we have a1 + 2d.

Our sequence is now:

a1, a1 + d, a1 + 2d

We continue this process and the resulting set of numbers is called an arithmetic progression (AP) or arithmetic sequence

Good Luck Telia

Sorry posted the comment and wasn't signed in.


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

Simba,

What are you working on multiplication?? Please clarify.

Telia


Marc 4 years ago

Find the next term of the progression 24,12,8,.....


miley 4 years ago

how do you find the equation and 50th term of 1,4,9,16,25,36,48


Kieran 4 years ago

What is the nth term for this sequence (or similar ones): 2, 7, 15, 26. It goes up like this: +5, +8, +9.


Carl 4 years ago

Hi would you be able to help me with the general term (tn) I guess, I doesn't know the word in english... well here are the numbers, 2,7,15,26,40 thanks :)


eivlys 4 years ago

Find the next term of the progression 2 4 6 14 23


rohit choudahry 4 years ago

0,2,4,6,8,12,12,20,16,?

answer is 12.

can u explain the trick behind this?


grace 4 years ago

what would be the nth term of 40,38,36,34,32...


joyce 4 years ago

what would be the nth term of 30,28,26,24,22... and what would be the nth term of 40,37,34,31,28...


joyce 4 years ago

what would be the nth term of 30,28,26,24,22..


arihant 4 years ago

what is the nth term of 1+(1+2)+(1+2+3).....to n terms


Simon 4 years ago

I'm stuck on this question so could you help me out?

All terms in a geometric sequence are positive integers, and the first three ter4ms are n, n+3, and 2n+6. What is the fourth term of this sequence?


Filip 4 years ago

-1 , -2 , -1 , 2 , 7 , 14 what's the nth term please?


Vin 4 years ago

What's The Next Three Terms of the Arithmetic Sequence?

6,12,18,24,__,___,___?

Help Please :D


akanksha raj 4 years ago

what will be the next term for this series 2,3,4,7,13,12,12,23,20,17,33,28,? please help.


shubham 4 years ago

iam confuse between nth and n terms of A.P

PLEASE HELP T.ELIA


Ronak 4 years ago

what will be the next term to the series 2,3,4,9,16... and how it will be???.....


Geralyn. 4 years ago

the radiator of the truck contains 12 gallons of water. We draw off 3 gallons and replace it with alcohol, then we draw off 3 gallons of the mixture then replaced it by alcohol. until 8 drawings and replacements have been dine. How much alcohol is in the final mixture?


t.elia 4 years ago

how bout sixth term of 3/4,3,12...


Anne David profile image

Anne David 4 years ago

what is the formula of sixth term of 3/4,3,12...


Anne David profile image

Anne David 4 years ago

and the tenth term of 0.4,0.04,0.004,,, plz give me a formula for this


sita 4 years ago

how to find the 40 term of a sequance with term to term rule add 5and the 1st term of 6


4 years ago

5 x 4 x 3 ... -5 x -2 x - 4 Write out the correct form of the sequence


4 years ago

What is the Nth Term to: -1, 7, 18, 29, 42, 57

and 2, 9, 18, 29, 42, 57?

Please help!


anonymous 4 years ago

given the general form an^2+bn+c

find a

pls help with the above


Charlott3_Fay3 4 years ago

What is 2-3G and 7-1/2n??? I'm really confused and it's annoying me please answer tonight xxxx


Jim 4 years ago

The nth term of a sequence is the l.c.m of integers from 1 to n. Which term of the sequence is the first one that's divisible by 100?


alicia 4 years ago

what is the 75th term 8, 14, 20, 26, 32


waleedrehman 4 years ago

plz find the indicated term of the following,1,3/2,5/4,7/8,...a7.


john 4 years ago

terms: 1,2,3,4,5,...n

values: 1,2,4,8,16,...

please find me the formula?


brittany 4 years ago

Can Anyone Find What's The 6th Term For 5 , 7 , 11 ....


paul 4 years ago

in an AP the fifth term is 8 and the nineth term is 14. fin the first term.


DIANA 4 years ago

WHAT IS THE FORMULER FOR THE SEQUENCE; 22,18,14,10?


dmndmz 4 years ago

Greetings ;)

What is the formula for the sequence 16, 29, 48, 52, 54 and 5 ?


Fazla 4 years ago

Maa''m i can't understand general term.. I don't knw why.. If u can help me in dis.. it will be a great help..

-2,4,-8,16.. can u help me 2 find da general term of dis set??


williamovely@yahoo.com 4 years ago

a series is s

uch that the sum of the first nth therms is 2n^2 minus 3n.

1.how to Prove that the series is arithmatic

2.find the value of the 18th term


CHRISTY 4 years ago

nth term of sequence ?7, ?21, 3?7.....


SURUTHI 4 years ago

HI,

pleasssssssse solve this problem ,i am not getting the solution anywhere in the net.

"the sum of the first n terms of an ap are in the ratio (3n +8):(7n + 15), find the ratio of the 3 rd terms" ans 23:50.


SURUTHI 4 years ago

HI,

pleasssssssse solve this problem ,i am not getting the SOLUTION anywhere in the net.

"the sum of the first n terms of an ap are in the ratio (3n +8):(7n + 15), find the ratio of the 3 rd terms"

{ans=23:50}.


Jimmy 4 years ago

nth term of sequence the sequence is 4, 12, 24

This is what i gett

4 12 24 40

\ / \ / \ /

8 12 16

\ / \ /

4 4

But I dont know how to make a formula from this help


Kalyanakrishnan 4 years ago

give solution to this sum

sum of the series 2+4(3*3)+6(5*5)+.........+22(21*21)


suruthi 4 years ago

if the sum of 4 consecutive terms in a gp is 60 and if the t1,18,t4 are in ap find the terms

ans(4,8,16,18)


Subhasish Raha 4 years ago

what is the missing number in the following series

9,19,40,___,146?


Lisa 4 years ago

trying to find out the correct sequence for if n+1/3


Helmi 4 years ago

how to solve this

U 1 2 3 4 5

Un 1 4 10 22 46


fawzy 4 years ago

plz define in detail what do we do with sequences not having a common difference E.G 0..-1..-8..-27..-64.

And also do you happen to know any formula like

Tn= A+d(n-1)+ 1/2[(n-1)(n-2)c] which claims to work on everything. If Yes than please explain the formula.


yaya 4 years ago

hi am year 7 what is the 5 terms and the 10th term of 2n+2


ragu 4 years ago

In the sequence, 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 when we add any three numbers we have to get the answer 30


Pavan Kumar 4 years ago

24 24 28 46 94 what is the next sequence


chris 4 years ago

An arithmetic sequence has first term a=6 and common difference d=12. How many terms of this sequence must be added to get 5040?


Adam Saleh 4 years ago

The nth term of a sequence is n^2-6n-4, find the sum of 3rd and 4th terms


Kyle 4 years ago

Which statement describes how to find the nth term in the sequence?

12, 29, 46, 63, 80, ...

A.add 5 times the term number and 12

B.subtract 17 times the term number from 12

C.subtract 5 from 17 times the term number

D.add 5 and 17 times the term number


luiza 4 years ago

Please help me

look at the equation n+3=12. Use iot to work out the value of n-3


met 4 years ago

what are the next two numbers 4, 5, 14, 15, 40, 41, _, _, ?


timmi2000 4 years ago

wondering if anyone could help me with these questions, and help me work it out as i do not seem to get it.

1) find the 8th term of each of these sequences

a) 2,5,8,11

b) 3,7,11,15

c) 2,10,50,250

d) 2,6,18,54

2) find the sum of the first 10 terms of the following series

a)3,8,13,18

b)1,3,9,27

3) the first term of an arithmetic series is 1. the common difference is 6 find the 10th term of the series, the sum of the first N terms is 7400 find N


Howard 4 years ago

what is the pattern of these numbers?

a)2,3,6,85,68

thank you


Kiki 4 years ago

Given the progression 7, 12, 17 and 22. What is the expression for the nth term of the progression?


Cherry 4 years ago

N term of these number 13,21,37,69,133. Please help


ray 4 years ago

what's 5 ways to find the 77th term?


tom 4 years ago

what's the nth term for 10, 40, 90, 160, 250, 360, 490...


kola 3 years ago

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=210


Naseem Choudhury 3 years ago

what is the term of 25-4n


becky 3 years ago

how would I solve for the nth term:

1+2=(2x3)/2

1+2+3=(3X4)/2

1+2+3+4=(4x5)/2


Rues 3 years ago

24,54,103,....


Telamon 3 years ago

what is the first 5 terms and the 100th term for the sequence whose rule is 0.5n - 0.5


Avicii 2 years ago

Does anybody on this goddamn blog answer questions!!!??


pooja 2 years ago

This website is boaring


wow 2 years ago

Not bad


thalene 2 years ago

the sum of the 17 term of an arithmetic sequence is 2414 and the last term is 256. find the first term


amberb 2 years ago

HELP ASAP the first 5 terms and the 100th term for the sequence 0.5n-0.5


john 19 months ago

find the nth term of 2n+5. find the frist term,second term and common difference

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