Find the wrong term in the number series: 3, 7, 16, 32, 56, 93, 142. Exactly one term violates a clean pattern; identify the incorrect term.

Difficulty: Easy

Correct Answer: 56

Explanation:


Introduction / Context:
Many number-series questions use steadily growing differences, often perfect squares. The task is to spot a single inconsistent entry.



Given Data / Assumptions:

  • Series: 3, 7, 16, 32, 56, 93, 142.
  • Assume a clean, deterministic rule with one misprint or anomaly.


Concept / Approach:
The natural hypothesis is “add consecutive squares”: +2^2, +3^2, +4^2, +5^2, +6^2, +7^2.



Step-by-Step Solution:

Start at 3.3 + 4 = 7 (2^2) ✔7 + 9 = 16 (3^2) ✔16 + 16 = 32 (4^2) ✔32 + 25 = 57 (5^2) → given 56 ✖Continuing the intended rule: 57 + 36 = 93 (6^2) ✔; 93 + 49 = 142 (7^2) ✔


Verification / Alternative check:
Replacing 56 by 57 restores perfect square-step differences through the tail, confirming a single early slip.



Why Other Options Are Wrong:
7, 16, and 32 each align exactly with the square-difference ladder. The inconsistency appears first at the fifth term only.



Common Pitfalls:
Confusing “nearby” values like 56 and 57; always compute the expected difference rather than eyeballing.



Final Answer:
56 is the wrong term (it should be 57 under +2^2, +3^2, +4^2, +5^2, +6^2, +7^2).

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