Identify the incorrect term in the following number series: 2, 7, 14, 23, 34,…

Concept

A useful way to test a number series is to subtract each term from the next and examine the sequence of consecutive differences.

When those differences follow consecutive odd numbers, each new term is obtained by adding the next odd increment.

Application

1. Compute the consecutive differences: 7 − 2 = 5, 14 − 7 = 7, 23 − 14 = 9, 34 − 23 = 11, and 48 − 34 = 14.

2. The first four differences are 5, 7, 9, and 11. They are consecutive odd numbers increasing by 2, so the next difference should be 13.

3. Using that difference, the final term should be 34 + 13 = 47. The recorded final term is 48.

Cross-check

Starting from 2 and successively adding 5, 7, 9, 11, and 13 gives 2, 7, 14, 23, 34, 47, which reproduces every earlier term and confirms the pattern.

Result

Therefore, the incorrect number in the given series is 48.