Complete the series using the recurring “double then ±1” pattern: 2, 5, 9, 19, 37, ( ? )

Introduction / Context:
Many series in aptitude tests toggle a small add/subtract around a doubling or tripling rule. Here the numbers suggest doubling plus or minus a small constant in an alternating fashion.

Given Data / Assumptions:

• Sequence: 2, 5, 9, 19, 37, ( ? )
• We suspect a pattern of doubling followed by ±1.

Concept / Approach:
Check terms pairwise: 2*2 + 1 = 5; 5*2 − 1 = 9; 9*2 + 1 = 19; 19*2 − 1 = 37. The sign flips each time: +1, −1, +1, −1. Hence the next step should again be +1.

Step-by-Step Solution:
2 → 5: 2*2 + 15 → 9: 5*2 − 19 → 19: 9*2 + 119 → 37: 19*2 − 137 → ( ? ): 37*2 + 1 = 75

Verification / Alternative check:
Continuing the alternating signs reproduces the earlier structure exactly, confirming 75 fits uniquely.

Why Other Options Are Wrong:
76 and 74 are off by ±1 from the correct doubling outcome; “None” is invalid since 75 matches.

Common Pitfalls:
Forgetting the sign alternation and using +1 repeatedly.

Final Answer:
75