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

Concept

In a square-based number series, a term of the form n2 − 1 is obtained by subtracting 1 from consecutive perfect squares.

Equivalently, successive terms increase by consecutive odd numbers because (n + 1)2 − n2 = 2n + 1.

Application

1. Add 1 to the given terms: 0, 1, 4, 9, 16, 25. These are 02, 12, 22, 32, 42, 52.

2. The next consecutive square is 62 = 36.

3. Subtracting 1 gives 36 − 1 = 35.

Cross-check

The successive differences are 1, 3, 5, 7, 9. The next consecutive odd difference is 11, and 24 + 11 = 35.

Therefore, the missing number is 35.