Number Series — Missing Term among Squares of Primes Find the missing number: 4, 9, 25, ?, 121, 169, 289, 361

Introduction / Context:This series contains perfect squares, specifically of consecutive prime numbers. Recognizing prime-based square progressions is a common exam theme.

Given Data / Assumptions:

• Numbers: 4, 9, 25, ?, 121, 169, 289, 361
• Check whether each is a perfect square and identify the base numbers.

Concept / Approach:Compute square roots to see if they align with consecutive primes. If so, the missing number should be the square of the prime that fits the sequence order.

Step-by-Step Solution:4 = 2^2 (prime 2)9 = 3^2 (prime 3)25 = 5^2 (prime 5)? should be 7^2 = 49 (prime 7)121 = 11^2 (prime 11)169 = 13^2 (prime 13)289 = 17^2 (prime 17)361 = 19^2 (prime 19)

Verification / Alternative check:All shown terms are squares of consecutive primes: 2, 3, 5, 7, 11, 13, 17, 19. The missing fourth term must be 49 to preserve order.

Why Other Options Are Wrong:

• 64 (8^2) and 81 (9^2) are not squares of primes; 8 and 9 are composite.
• 87 is not a perfect square.

Common Pitfalls:Assuming numerical proximity instead of verifying the structural rule (squares of primes). Always test the roots and primality of the bases.

Final Answer:49