Math CentralQuandaries & Queries


Question from Ting, a student:

The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please)

Hi Ting,

The two sequences begin

1 &  5& &14& &  30&\\
4 &20& &56& &120&

How does each term of the second sequence relate to the corresponding term of the first sequence?


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