In the decreasing sequence 52, 51, 48, 43, 34, 27, 16, which one term is wrong because it does not follow the regular subtraction pattern?

Introduction / Context:
This question presents a decreasing series of numbers and asks you to identify which one does not fit a simple subtraction pattern. Such questions test your ability to detect consistent differences between consecutive terms and to spot a single anomaly in that pattern.

Given Data / Assumptions:
The sequence is 52, 51, 48, 43, 34, 27, 16. We assume that the intended sequence follows a simple rule involving subtracting odd numbers in a recognizable order. Exactly one term is assumed to be incorrect.

Concept / Approach:
When a series decreases, it is natural to check the differences between successive terms. Often, those differences themselves follow a simple pattern, such as successive odd numbers: 1, 3, 5, 7, 9, etc. Identifying this pattern allows us to see which term breaks the rule.

Step-by-Step Solution:
Step 1: Compute consecutive differences.52 → 51: difference = -1.51 → 48: difference = -3.48 → 43: difference = -5.43 → 34: difference = -9.34 → 27: difference = -7.27 → 16: difference = -11.Step 2: Compare these differences with the ideal sequence of consecutive odd numbers: -1, -3, -5, -7, -9, -11.Step 3: Up to 48 → 43, the pattern matches -1, -3, -5. The next odd numbers should be -7, -9, -11 in that order.Step 4: From 43, subtracting 7 should give 36, not 34. Then 36 - 9 = 27 and 27 - 11 = 16 would perfectly match the remaining terms.Step 5: Therefore, the term that should be 36 has been incorrectly written as 34. The incorrect term in the series is 34.

Verification / Alternative check:
Reconstruct the corrected series using the intended pattern of subtracting consecutive odd numbers: 52 - 1 = 51, 51 - 3 = 48, 48 - 5 = 43, 43 - 7 = 36, 36 - 9 = 27, 27 - 11 = 16. This gives the sequence 52, 51, 48, 43, 36, 27, 16, which is perfectly regular. Only the originally given value 34 breaks this structure.

Why Other Options Are Wrong:
52, 51 and 27 all fit correctly into the consistent pattern of subtracting consecutive odd numbers. Changing any of them would disrupt several differences at once and would not restore a clean sequence. The only single change that makes the pattern fully correct is replacing 34 with 36, so 34 must be the wrong term.

Common Pitfalls:
Students sometimes look only at approximate size changes and miss the exact sequence of odd-number differences. Another frequent error is to miscalculate one or more of the differences, which can hide the underlying pattern. Writing out each difference clearly is essential for accurate reasoning.

Final Answer:
The term that does not follow the intended subtraction pattern is 34.