Introduction / Context:
Odd-one-out series often rely on steadily increasing differences. If one term slightly deviates, it signals the outlier. Here we analyze first- and second-order differences to confirm which value does not belong.
Given Data / Assumptions:
- Series: 8, 13, 21, 32, 47, 63, 83
- Exactly one term is incorrect.
Concept / Approach:
Compute consecutive differences; look for a smooth pattern (e.g., +5, +7, +9, +11, +13, etc.). A single break in the smoothness usually identifies the odd term.
Step-by-Step Solution:
Differences: 13−8 = 521−13 = 832−21 = 1147−32 = 1563−47 = 1683−63 = 20Up to 32 the increments grow by +3 each time: +5, +8, +11. Continuing that idea gives +14, +17, +20…Expected continuation from 32 would be 32 + 14 = 46 (not 47), then +17 to 63, then +20 to 83.Thus 47 is 1 unit higher than the smooth pattern suggests and is the outlier.
Verification / Alternative check:
Reconstructed smooth series: 8, 13, 21, 32, 46, 63, 83.Only 47 disagrees with the target pattern.
Why Other Options Are Wrong:
63 and 83 fit the projected +17 and +20 steps; 32 matches earlier growth. They are consistent.
Common Pitfalls:
Assuming Fibonacci-like rules; here, differences—not term sums—govern the sequence.
Final Answer:
47
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