Find the missing term in the given series: 16, 20, 25, 30, 36, 42, 49, ?

Concept

A sequence may interleave two related forms generated from each integer n. To identify the rule, group adjacent terms and test whether they follow n2 and n(n + 1).

Application

1. For n = 4, the pair is 42 = 16 and 4 × 5 = 20.

2. For n = 5, the pair is 52 = 25 and 5 × 6 = 30.

3. For n = 6, the pair is 62 = 36 and 6 × 7 = 42.

4. For n = 7, the first term is 72 = 49, so its companion term is 7 × 8 = 56.

Cross-check

The successive differences are 4, 5, 5, 6, 6, 7; repeating 7 gives 49 + 7 = 56. Thus the missing term is 56.