What will be the next term in the following number series? 0, 8, 24, 48, …?

Concept

In a number series, inspect the differences between consecutive terms.

When the first differences follow a regular pattern, extend that difference pattern first and then add the next difference to the last term.

Application

1. Compute the consecutive differences: 8 − 0 = 8, 24 − 8 = 16, and 48 − 24 = 24.

2. The differences are 8, 16, 24; each new difference is 8 more than the preceding one.

3. Therefore, the next difference is 24 + 8 = 32.

4. Add this to the last term: 48 + 32 = 80.

Cross-check

The terms also follow 4n(n − 1) for n = 1, 2, 3, …: 0, 8, 24, 48, 80. Thus, the next term is 80.