Find the wrong number in the series given below: 3, 8, 13, 21, 31, 43

Concept

In a number series, inspect the first differences between consecutive terms. A regular arithmetic pattern can be identified when those differences themselves follow a simple sequence.

Application

1. Test the rule in which consecutive differences are the even numbers +4, +6, +8, +10, and +12.

2. Starting from 3, adding 4 gives 7, not 8.

3. Continuing from 7, adding 6, 8, 10, and 12 gives 13, 21, 31, and 43 respectively.

Cross-check and result

The corrected series 3, 7, 13, 21, 31, 43 has successive differences 4, 6, 8, 10, 12. Therefore, the wrong term in the displayed series is 8.