Wrong Term in the Prime-Square Series: 529, 841, 961, 1296, 1681, 1849, 2209 — identify the term that breaks the pattern (squares of consecutive odd primes).

Introduction / Context:Square-number series often use squares of consecutive integers or, more specifically, consecutive primes. Here, most terms are squares of consecutive odd primes.

Given Data / Assumptions:

• 529 = 23^2
• 841 = 29^2
• 961 = 31^2
• 1296 = 36^2
• 1681 = 41^2
• 1849 = 43^2
• 2209 = 47^2

Concept / Approach:Identify whether each term is the square of a consecutive odd prime: 23, 29, 31, 37, 41, 43, 47.

Step-by-Step Solution:529 → 23^2 ✓841 → 29^2 ✓961 → 31^2 ✓1296 → 36^2 (not prime) ✗1681 → 41^2 ✓1849 → 43^2 ✓2209 → 47^2 ✓

Verification / Alternative check:If the intended missing prime were 37, its square would be 1369, not 1296. Hence 1296 is the unique misfit.

Why Other Options Are Wrong:

• 529, 841, 961, 1681: each is p^2 for odd primes (23, 29, 31, 41).

Common Pitfalls:Assuming “consecutive squares” instead of “squares of consecutive odd primes.” 36 is composite, so 36^2 breaks the prime-square motif.

Final Answer:1296