Find the next three terms of the following sequence.

(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.