Number series (find the wrong term): 196, 169, 144, 121, 100, 80, 64 Exactly one term does not follow the underlying rule. Identify it and justify your choice.

Introduction / Context:This sequence looks like perfect squares listed in decreasing order. Such patterns are common in number reasoning tests. We must find the one term that is not a perfect square in the correct descending progression.

Given Data / Assumptions:

• Series: 196, 169, 144, 121, 100, 80, 64
• One term is erroneous.

Concept / Approach:Recall perfect squares: 14^2 = 196, 13^2 = 169, 12^2 = 144, 11^2 = 121, 10^2 = 100, 9^2 = 81, 8^2 = 64. The intended pattern appears to be descending squares 14^2 down to 8^2.

Step-by-Step Solution:Map each term to a square: 196 = 14^2 ✔, 169 = 13^2 ✔, 144 = 12^2 ✔, 121 = 11^2 ✔, 100 = 10^2 ✔.Next should be 9^2 = 81, but the series shows 80.Finally, 64 = 8^2 ✔. Therefore, 80 is the only non-square and is the wrong term.

Verification / Alternative check:Replace 80 with 81 and the sequence becomes consecutive perfect squares: 196, 169, 144, 121, 100, 81, 64.

Why Other Options Are Wrong:

• 169, 144, 121, 100: All are correct perfect squares in order.
• 80: Not a perfect square and disrupts the descending-square pattern.

Common Pitfalls:Some candidates misremember 9^2 as 80 instead of 81 or overlook one term in a long list. Always check each term against its square root.

Final Answer:80