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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