Find the next three terms of the following sequence. (iii) 1/4, 2/9, 3/16,…

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.

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