Number series – Find the wrong number (double then add n) 3, 7, 16, 35, 72, 153, 312 Exactly one term is incorrect. Identify the term that breaks the rule “a(n) = 2*a(n−1) + n”.

Introduction / Context:
A common construction is a(n) = 2*a(n−1) + n, where n starts at 1 for the first transition and increases by 1 each step. One erroneous term typically disrupts the clean recurrence.

Given Data / Assumptions:

• Series: 3, 7, 16, 35, 72, 153, 312
• Hypothesized rule: a(n) = 2*a(n−1) + n with n = 1, 2, 3, …

Concept / Approach:
Apply the recurrence term-by-term and locate the violation.

Step-by-Step Solution:
From 3: 2*3 + 1 = 7 → OK.From 7: 2*7 + 2 = 16 → OK.From 16: 2*16 + 3 = 35 → OK.From 35: 2*35 + 4 = 74 → the series shows 72 → wrong here.Continuing with corrected 74: 2*74 + 5 = 153 → OK; 2*153 + 6 = 312 → OK.

Verification / Alternative check:
With “74” in place of “72,” the recurrence holds across the whole sequence, so “72” is the only error.

Why Other Options Are Wrong:

• 7, 35, 153 → all consistent once the single error is fixed.
• None of these → incorrect because “72” uniquely breaks the rule.

Common Pitfalls:
Using n = 0 at the first step; this series clearly starts with n = 1 (giving +1 at the first transition).

Final Answer:
72