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

CONCEPT

In a difference series, subtract consecutive terms to obtain first differences.

If these are not regular, compare consecutive first differences again. A pattern in the second differences determines the next first difference.

APPLICATION

1. The first differences are 11 − 5.5 = 5.5, 18.5 − 11 = 7.5, 30 − 18.5 = 11.5, 49.5 − 30 = 19.5, and 85 − 49.5 = 35.5.

2. The second differences are 7.5 − 5.5 = 2, 11.5 − 7.5 = 4, 19.5 − 11.5 = 8, and 35.5 − 19.5 = 16.

3. These second differences double each time, so the next second difference is 32.

4. Therefore, the next first difference is 35.5 + 32 = 67.5, and the next term is 85 + 67.5 = 152.5.

CROSS-CHECK

Substituting 152.5 gives the new first difference 152.5 − 85 = 67.5 and the new second difference 67.5 − 35.5 = 32, continuing 2, 4, 8, 16, 32.

Result: 152.5.