# FINDING THE nth TERM IN A SEQUENCE

## Formula's for the nth term

Here I intend to look at what is known as the **n ^{th}**

**term**sequence. In doing so we will look at some examples and find the

**n**which is known in mathematical terms by a

^{th }term**"u"**followed by a subscript(small)

_{"}_{n}_{"}_{}.

So what exactly is the connection( the pattern) between the **"n"** and the **"u _{n}".**

If we take a closer look at the **u _{n }**

_{}we can see that it goes up in

**two's (2's).**

**(Position) U 1 2 3 4 5**

** ( Term) U _{n }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 **u _{n }= 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 multiplying**n x 2**, you will have noticed that they are **1 **less in each case than the numbers in the **u _{n}**

_{}bracket, therefore we need to

**add on 1**in the formula.

Our formula now looks like this **u _{n }= 2n + 1 (where the u_{n }is the n^{th }term)**

**2 x n = ? + 1 = u _{n}**

**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:- u _{n }= 2n + 1**

**This is the type of question for the n ^{th }^{}term, could be asked in an exam paper;**

**Find the n ^{th} 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 “u _{n}” 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) U _{n }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 "u _{n}", in this question?**

**If we take a closer look at the "u _{n}" 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** **u _{n }= 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 u _{n }term, therefore we need to subtract 2 in the formula.**

**Our formula now looks like this; u _{n }= 4n - 2 (where the u_{n}_{}is the n^{th }term)**

**4 x n = ? - 2 = u _{n }**

**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:- u _{n }= 4n - 2**

**In this example we need to find the n ^{th }term for this sequence;**

**Find the n ^{th} 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 “u _{n}“ 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) U**_{n }**3 6 11 18 27**

**n ^{2}=(n x n) 1 4 9 16 25 **

**So what exactly is the connection (the pattern ) between the "n" and the "u _{n}", 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 (**n ^{2}**) the numbers and see what that brings us too.

**Therefore we can write down that u _{n }= n^{2} (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 u _{n }term, therefore we need to add 2 in the formula.**

**Our formula now looks like this; u _{n }= n^{2} + 2 ( where the u_{n }is the n^{th }term)**

**n x n = ? + 2 = u _{n}**

**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:- u _{n }= n^{2} + 2 **

**Another favourite question in exams is as follows;**

**The n ^{th }term of a sequence is represented by this formula:- u_{n }= 3n + 2**

**We are asked to;**

**(i) Find the first 4 terms**

**(ii) To find the 49^{th} term **

**( i ) Find the first 4 terms**

**Our formula is:- 3n + 2 = u _{n }**

**Therefore our 1 ^{st} term is u_{1} = 3 x 1 = 3 + 2 = 5**

** 2 ^{nd} term u_{2 }= 3 x 2 = 6 + 2 = 8**

** 3 ^{rd} term u_{3 }= 3 x 3 = 9 + 2 = 11**

** 4 ^{th} term u_{4 }= 3 x 4 = 12 + 2 = 14**

**Our first four terms are; u _{1} , u_{2} , u_{3 }, and u_{4 }**

**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 49 ^{th} term. **

**49 ^{th} term: This will be known as u_{49}**

**As before in part ( i ) the formula is; u _{n }= 3n + 2 **

**Therefore we will replace the “ _{n}” with the 49**

** u _{n }= 3n + 2**

**u _{49 }= (3 x 49) = 147 + 2 = 149**

**(Answer) u _{49 }= 149**

## More by this Author

- 2
In this hub I intend to establish the relationship between "powers" and fractions in the nth term of a sequence. Complete the tables below given that the nth term is: (i) We will complete...

- 7
What is a Matrix? A matrix is defined as an ordered rectangular array of numbers. They can be used to represent systems of linear equations. They are a key tool in linear Algebra. This ordered array...

- 8
In this hub we are going to be looking at the different parts of a circle and how to calculate each of them. The Circumference of a Circle, this is the perimeter of a...

## Comments 258 comments

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

Really good one,very neatly explained with relevent examples

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

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

7, 10, 13, 16, 19 :)

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.

what is nth term for squared numbers

whaat is the nth term of 4 6 8 10

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

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

how about this one. find the 9th term

n2/n+1

find a formula for 95, 90, 85,80

interms of n

gd website

what will be the nth term in this sequence

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

Help!!!

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

me!!!

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

where:

tn = general term

a = first term

r = common ratio

n = position of the term

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

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

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 :)

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

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

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

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

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

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

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

??????

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

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

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

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

Help please how is this worked out

first term 4 term to term rule x3 +1

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.

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?

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.

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?

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.

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

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?"

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...

Thanks a lot..

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

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

wow !

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

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

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

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.

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

nive post. really helped.

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

Please help meee :(

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.

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

and 19,13,7,1,-5

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

thanks!

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

please help find the next three sequence

20,4,16,37

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

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

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

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

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

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? :)

position: 1 2 3 4 5 6

value of : 5 14 23 32 ??

term

really helpful

help me to solve this:

(28% - 8%) / 1.4 = ?

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

The nth term of a sequence is 100-2n

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

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

Thanks

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

whats the nth term of 4,8,16

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?

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

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

i know it is adding multiples of 8 each time

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

11,9,7,5,3,1

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

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

thanks.

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

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

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

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

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

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

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)?

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 .

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

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

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

Im really confused!

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

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

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

Doing my GCSEs and stuck on homework.

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

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

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

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

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 .

26-4n?

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

can you solv please 7,10,13,16

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

Hi, can you help me.

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

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

hello plaese help me find Recurrence Relations

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

thank you so much

i keep forgetting that n means term number!!!

WHAT IS AP?

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

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

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

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 :)

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

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

answer is 12.

can u explain the trick behind this?

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

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...

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

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

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?

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

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

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

Help Please :D

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

iam confuse between nth and n terms of A.P

PLEASE HELP T.ELIA

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

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?

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

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

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

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

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

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

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

Please help!

given the general form an^2+bn+c

find a

pls help with the above

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

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?

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

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

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

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

please find me the formula?

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

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

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

Greetings ;)

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

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??

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

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

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.

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}.

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

give solution to this sum

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

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)

what is the missing number in the following series

9,19,40,___,146?

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

how to solve this

U 1 2 3 4 5

Un 1 4 10 22 46

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.

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

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

24 24 28 46 94 what is the next sequence

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?

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

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

Please help me

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

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

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

what is the pattern of these numbers?

a)2,3,6,85,68

thank you

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

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

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

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

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

what is the term of 25-4n

how would I solve for the nth term:

1+2=(2x3)/2

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

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

24,54,103,....

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

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

This website is boaring

Not bad

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

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

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

258