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.

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:

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).