Find the wrong term in the number series: 0, 1, 9, 36, 99, 225, 441. The intended rule is “square of triangular numbers”: Tn^2 where Tn = 0,1,3,6,10,15,21… Identify the incorrect term.

Question

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

Accepted Answer

Introduction / Context:Many classic series use triangular numbers Tn = n*(n+1)/2 and then apply a transformation such as squaring. Here, terms visibly align with Tn^2—except one. Given Data / Assumptions: Series: 0, 1, 9, 36, 99, 225, 441. Triangular numbers: 0, 1, 3, 6, 10, 15, 21… Squares: 0^2=0, 1^2=1, 3^2=9, 6^2=36, 10^2=100, 15^2=225, 21^2=441. Concept / Approach:Map each series term to Tn^2. All match perfectly except the 5th term. Step-by-Step Solution: 0 → 0^2 = 0 ✔1 → 1^2 = 1 ✔9 → 3^2 = 9 ✔36 → 6^2 = 36 ✔99 → should be 10^2 = 100 ✖225 → 15^2 = 225 ✔441 → 21^2 = 441 ✔ Verification / Alternative check:Once 99 is corrected to 100, the entire sequence becomes a clean Tn^2 progression without exception. Why Other Options Are Wrong:9, 36, and 225 correctly correspond to 3^2, 6^2, and 15^2. Common Pitfalls:Overlooking the triangular-index pattern and testing random square bases; always check Tn = 0,1,3,6,10… Final Answer:99 is the wrong term (should be 100).

Find the wrong term in the number series: 0, 1, 9, 36, 99, 225, 441. The intended rule is “square of triangular numbers”: Tn^2 where Tn = 0,1,3,6,10,15,21… Identify the incorrect term.

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