Find the number that can replace the question mark (?) in the series below: 4,…

Concept

In a number series, compare consecutive terms to identify the rule governing their differences. If the first differences themselves form an arithmetic sequence, extend that difference sequence before finding the next term.

Application

1. The consecutive differences are 10 − 4 = 6, 20 − 10 = 10, 34 − 20 = 14, 52 − 34 = 18, and 74 − 52 = 22.

2. These differences increase by 4 each time, so the next difference is 22 + 4 = 26.

3. Add this difference to the last term: 74 + 26 = 100.

Cross-check

The terms follow an = 2n2 + 2. For n = 6, this gives 74; for n = 7, it gives 100, confirming the continuation.

Therefore, the required number is 100.