In the number series 8, 15, 28, 53, ?, which term should replace the question mark to continue the pattern?

Introduction / Context:
This series grows faster than a simple arithmetic progression but not as fast as a pure geometric progression. This often indicates that the differences between terms themselves follow a multiplicative or doubling based pattern. Identifying this pattern allows us to calculate the missing term accurately.

Given Data / Assumptions:
- The series is: 8, 15, 28, 53, ?- All terms are positive integers.- The differences between terms appear to be increasing.

Concept / Approach:
We start by calculating the differences between consecutive terms. If these differences follow a recognisable recurrence, such as doubling minus a constant, we extend that rule to find the next difference. Adding that next difference to the last known term then yields the missing number in the original series.

Step-by-Step Solution:
- Compute differences: 15 - 8 = 7, 28 - 15 = 13, 53 - 28 = 25.- So the differences are: 7, 13, 25.- Examine the pattern: 7 * 2 - 1 = 13, and 13 * 2 - 1 = 25.- This suggests the rule difference(n+1) = 2 * difference(n) - 1.- Apply the rule to find the next difference: 25 * 2 - 1 = 50 - 1 = 49.- Add this next difference to the last term: 53 + 49 = 102.- Therefore, the missing term is 102.

Verification / Alternative check:
- Reconstruct using the rule starting from first difference 7: differences become 7, 13, 25, 49.- Build the series: 8 + 7 = 15, 15 + 13 = 28, 28 + 25 = 53, 53 + 49 = 102.- These values match the given terms and the newly computed term, confirming the pattern.

Why Other Options Are Wrong:
- 106, 100, and 108 cannot be obtained from 53 by adding a difference that fits the recurrence difference(n+1) = 2 * difference(n) - 1.- Substituting any of these would break the coherent pattern in the differences and yield inconsistent future terms.- Only 102 aligns perfectly with the discovered rule.

Common Pitfalls:
Sometimes candidates attempt to find a single formula that maps term position directly to term value without first checking the much simpler difference pattern. Others miscalculate the double minus one relation and end up with incorrect intermediate differences. Carefully compute each step and always verify by reconstructing the entire series.

Final Answer:
The correct term that should replace the question mark is 102, so the correct option is 102.