Find the wrong term in the number series: 5, 8, 16, 26, 50, 98, 194. A consistent rule from the beginning should be “next = 2 × previous − 2”. Identify the incorrect entry.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:We test a simple affine recurrence that fits almost all steps: multiply by 2 and subtract 2. Given Data / Assumptions: Series: 5, 8, 16, 26, 50, 98, 194. Candidate rule: a(n+1) = 2*a(n) − 2. Concept / Approach:Check each transition under the rule and locate the earliest violation. Step-by-Step Solution: 5 → 8: 2*5 − 2 = 8 ✔8 → 16: 2*8 − 2 = 14 ✖ (given 16)If we correct to 14, then 14 → 26: 2*14 − 2 = 26 ✔26 → 50: 2*26 − 2 = 50 ✔50 → 98: 2*50 − 2 = 98 ✔98 → 194: 2*98 − 2 = 194 ✔ Verification / Alternative check:Only the second step fails; fixing 16 to 14 repairs the entire tail perfectly. Why Other Options Are Wrong:26, 50, and 98 all satisfy the rule when the earlier misprint is corrected. Common Pitfalls:Mistaking downstream consistency for independent correctness; the first inconsistency typically identifies the wrong term. Final Answer:16 is the wrong term (should be 14).

Find the wrong term in the number series: 5, 8, 16, 26, 50, 98, 194. A consistent rule from the beginning should be “next = 2 × previous − 2”. Identify the incorrect entry.

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