Find the missing number in the series: 3, 5, 9, 17, ___

Concept: In a number series where the differences between consecutive terms themselves form a geometric progression, the difference doubles at each step (e.g. 2, 4, 8, 16, ... i.e. 2¹, 2², 2³, 2⁴). Once this pattern is confirmed on the differences, the next term is found by adding the next difference in the progression to the last given term.

Application: Compute the successive differences of the given series 3, 5, 9, 17:

1. 5 − 3 = 2 = 2¹

2. 9 − 5 = 4 = 2²

3. 17 − 9 = 8 = 2³

4. Following the pattern, the next difference = 2⁴ = 16

5. Missing term = 17 + 16 = 33

Cross-check: The differences 2, 4, 8, 16 form a geometric progression with common ratio 2, confirming the doubling rule holds consistently across all four gaps, so the value 33 completes the series correctly.