HOW TO FIND THE NEXT THREE TERMS IN A 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.

4^th term  =  3 (72)  =  216

5^th term  =  216 (3)  =  648

6^th term  =  648(3)  =  1944

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

(ii) 5, 1,-3,…

Solution :

Pattern :

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

4^th term  =  -3 - 4  =  -7

5^th term  =  -7 - 4  =  -11

6^th 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 n th term of the sequence is given ?

Question 2 :

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

(i) a_n = n³ −2

Solution :

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

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

(ii) a_n = (−1)ⁿ⁺¹ n(n + 1)

Solution :

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

(iii) a_n = 2n² - 6

Solution :

Hence the four terms are -4, 2, 12, 26.

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