The missing number in the series : 0, 6, 24, 60, 120, ?, 336, is

Concept

When a number series is generated by a product of consecutive integers, write its nth term in a general form and test that form against several known terms.

A consistent rule must account for every displayed term and must also predict the term after the blank.

Application

1. Index the terms from n = 0 and test an = n(n + 1)(n + 2).

2. For n = 0, 1, 2, 3, and 4, the products are 0×1×2 = 0, 1×2×3 = 6, 2×3×4 = 24, 3×4×5 = 60, and 4×5×6 = 120.

3. The blank is the term for n = 5, so a5 = 5×6×7 = 210.

Cross-check

The next term predicted by the same rule is a6 = 6×7×8 = 336, which matches the term shown after the blank.

Therefore, the missing number is 210.