Wrong Term in the Fibonacci-Sum Style Series: 13, 14, 27, 45, 68, 109, 177 — exactly one term is incorrect. Identify the wrong term and justify your choice by revealing the intended rule (each term should be the sum of the previous two).

Introduction / Context:In many number-series questions, the guiding rule is that each term equals the sum of the two preceding terms (a Fibonacci-like construction). Detecting one violation pinpoints the wrong term.

Given Data / Assumptions:

• Series as given: 13, 14, 27, 45, 68, 109, 177.
• Exactly one term is erroneous; the rest must follow a single consistent rule.

Concept / Approach:Test the Fibonacci-sum rule a(n) = a(n-1) + a(n-2). If the rule holds everywhere except at one index, that index is the wrong term.

Step-by-Step Solution:Check 3rd term: 13 + 14 = 27 ✓Check 4th term: 14 + 27 = 41 ≠ 45 → mismatchAssuming the rule is correct, the 4th term should be 41, not 45.Continue with corrected term (41): 27 + 41 = 68 ✓41 + 68 = 109 ✓68 + 109 = 177 ✓

Verification / Alternative check:With only the 4th term corrected to 41, the remainder of the sequence fits the rule perfectly. No other single change yields full consistency.

Why Other Options Are Wrong:

• 27: equals 13 + 14, hence correct.
• 68: equals 27 + 41 (with repaired 4th term), hence consistent.
• 109: equals 41 + 68, hence consistent.
• 177: equals 68 + 109, hence consistent.

Common Pitfalls:Stopping at the first mismatch and changing the preceding term. The minimal-change strategy is to change the mismatching term itself (45 → 41).

Final Answer:45