Find the next term in the series given below. 124, 148, 196, 268, 364, ?

Concept

In a number series, compare consecutive terms to expose the governing pattern. If the first differences themselves form an arithmetic sequence, extend that difference sequence by its common increment.

Application

1. 148 − 124 = 24.

2. 196 − 148 = 48.

3. 268 − 196 = 72.

4. 364 − 268 = 96.

5. The differences 24, 48, 72, 96 rise by 24 each time, so the next difference is 96 + 24 = 120.

6. The next term is 364 + 120 = 484.

Cross-check

The second differences are all 24: 48 − 24 = 24, 72 − 48 = 24, 96 − 72 = 24, and 120 − 96 = 24. Thus 484 continues the same rule.

The next term is 484.