Locate the wrong term in a “subtract consecutive odds” pattern: 52, 51, 48, 43, 34, 27, 16, …

Introduction / Context:
A classic decreasing series subtracts consecutive odd numbers: −1, −3, −5, −7, −9, −11, … Detecting one misstep among these consistent decrements identifies the odd term out.

Given Data / Assumptions:

• Sequence: 52, 51, 48, 43, 34, 27, 16, …
• Expected rule: subtract consecutive odd numbers.
• Exactly one number is incorrect.

Concept / Approach:
Compute differences and compare to the sequence of odd numbers 1, 3, 5, 7, 9, 11. A deviation from this list pinpoints the wrong value.

Step-by-Step Solution:
52 − 51 = 1 (odd 1)51 − 48 = 3 (odd 3)48 − 43 = 5 (odd 5)43 − 34 = 9 (should have been 7 if strictly consecutive)Proper step: 43 − 7 = 36 (not 34)Continuing: 36 − 9 = 27, 27 − 11 = 16

Verification / Alternative check:
Once 34 is corrected to 36, all decrements line up perfectly with 1, 3, 5, 7, 9, 11. The given 27 and 16 already align with the corrected course, confirming that 34 is the only anomaly.

Why Other Options Are Wrong:

• 48 / 43 / 27: each respects the consecutive-odd subtraction once the earlier correction is made.

Common Pitfalls:

• Mistaking a single out-of-order odd decrement (9 vs 7) as a wholesale pattern change.

Final Answer:
34