Number Series — Double and Add One Pattern Find the missing term: 3, 7, 15, ?, 63, 127

Introduction / Context:This is a rapidly growing series governed by the simple rule: multiply by 2, then add 1. Such patterns appear frequently in aptitude tests due to their clarity and speed of computation.

Given Data / Assumptions:

• Series: 3, 7, 15, ?, 63, 127
• Look for consistent multiplicative growth with a small additive constant.

Concept / Approach:Test whether each step follows the same operation: next = current * 2 + 1. If confirmed, apply it to the missing position.

Step-by-Step Solution:3 * 2 + 1 = 77 * 2 + 1 = 15Therefore missing term = 15 * 2 + 1 = 31Check forward: 31 * 2 + 1 = 6363 * 2 + 1 = 127

Verification / Alternative check:All visible transitions obey the same rule consistently, so 31 is uniquely determined by the pattern.

Why Other Options Are Wrong:

• 30, 47, 52: Substituting any of these breaks one or more steps of the rule when continued forward.

Common Pitfalls:Misreading the pattern as +4, +8, +16, etc. Always test multiplicative rules directly before exploring changing differences in such fast-growing sequences.

Final Answer:31