# 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**

## Comments

what is the nth term of 12,23,36,51,68

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

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

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

Not bad

This website is boaring

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

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

24,54,103,....

how would I solve for the nth term:

1+2=(2x3)/2

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

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

what is the term of 25-4n

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

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

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

what is the pattern of these numbers?

a)2,3,6,85,68

thank you

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

Please help me

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

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

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

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?

24 24 28 46 94 what is the next sequence

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

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

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.

how to solve this

U 1 2 3 4 5

Un 1 4 10 22 46

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

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9,19,40,___,146?

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)

give solution to this sum

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

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

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 ?7, ?21, 3?7.....

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

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??

Greetings ;)

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

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

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

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

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

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

please find me the formula?

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

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

given the general form an^2+bn+c

find a

pls help with the above

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

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

Please help!

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

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

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

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

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?

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

iam confuse between nth and n terms of A.P

PLEASE HELP T.ELIA

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

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

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

Help Please :D

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

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?

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

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

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 40,38,36,34,32...

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

answer is 12.

can u explain the trick behind this?

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

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 :)

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

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

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

WHAT IS AP?

i keep forgetting that n means term number!!!

thank you so much

hello plaese help me find Recurrence Relations

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

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:ap2t.../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

Hi, can you help me.

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

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

can you solv please 7,10,13,16

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

26-4n?

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 .

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

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

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

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

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

Doing my GCSEs and stuck on homework.

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

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

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