# HOW TO FIND THE NEXT THREE TERMS IN A SEQUENCE

## About "How to Find the Next Three Terms in a Sequence"

How to Find the Next Three Terms in a Sequence :

Here we are going to see some practice questions to find the next three terms in a sequence.

## What is Sequence ?

There is some arrangement or pattern followed in every sequence.

There are two types of sequence,

Finite sequence :

If the number of elements in a sequence is finite then it is called a Finite sequence.

Infinite sequence :

If the number of elements in a sequence is infinite then it is called an Infinite sequence.

Question 1 :

Find the next three terms of the following sequence.

(i) 8, 24, 72, …

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

Multiplying the first term by 3, we get the second term.Multiplying the second term by 3, we get the third term.

4th term  =  3 (72)  =  216

5th term  =  216 (3)  =  648

6th term  =  648(3)  =  1944

Hence the next three terms are 216, 648, 1944.

(ii) 5, 1,-3,…

Solution :

Pattern :

By subtracting 4 from the 1st term, we get second term. By subtracting 4 from 2nd term, we get 3rd term.

4th term  =  -3 - 4  =  -7

5th term  =  -7 - 4  =  -11

6th term  =  -11 - 4  =  -15

Hence the next three terms are -7, -11, -15.

(iii) 1/4, 2/9, 3/16,…

Solution :

Pattern :

General term  =  n [1/(n + 1)]2

n is elements of natural numbers.

4th term  =  4 [1/(4 + 1)]2

=  4[1/5]2

=  4/25

5th term  =  5 [1/(5 + 1)]2

=  5[1/6]2

=  5/36

6th term  =  6 [1/(6 + 1)]2

=  6[1/7]2

=  6/49

Hence the next three terms are 4/25, 5/36, 6/49.

## How to find next four terms if nth term of the sequence is given ?

Question 1 :

Find the first four terms of the sequences whose nth terms are given by

(i) an = n3 −2

Solution :

To find the 1st term, we have to apply n = 1

 an = n3 −2n = 1a1 = 13 −2  =  1 -  2a1  =  -1 an = n3 −2n = 2a2 = 23 −2  =  8 -  2a2  =  6 an = n3 −2n = 3a3 = 33 −2  =  27 -  2a3  =  25 an = n3 −2n = 4a4 = 43 −2  =  64 -  2a4  =  62

Hence the first four terms are -1, 6, 25, 62.

(ii) an = (−1)n+1 n(n + 1)

Solution :

 an = (−1)n+1 n(n + 1)n = 1=  (−1)n+1 n(n + 1)=  (−1)1+1 1(1 + 1)=  1 (2)a1  =  2 n = 2=  (−1)n+1 n(n + 1)=  (−1)2+1 2(2 + 1)=  -1 (6)a2  =  -6 n = 3=  (−1)n+1 n(n + 1)=  (−1)3+1 3(3 + 1)=  1 (12)a3  =  12 n = 4=  (−1)n+1 n(n + 1)=  (−1)4+1 4(4 + 1)=  -1 (20)a4  =  -20

Hence the first four terms are 2, -6, 12, -20.

(iii) an = 2n2 - 6

Solution :

 an = 2n2 - 6n = 1=  2(1)2 - 6a1  =  -4 an = 2n2 - 6n = 2=  2(2)2 - 6a2  =  2 an = 2n2 - 6n = 3=  2(3)2 - 6a3  =  12 an = 2n2 - 6n = 4=  2(4)2 - 6a4  =  26

Hence the four terms are -4, 2, 12, 26. After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Next Three Terms in a Sequence".

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