Question:
Find the next number in series: 4, 9, 25, 49, 121, 169, 289, ?,529
Find the next number in series: 4, 9, 25, 49, 121, 169, 289, ?,529
Show Hint
If numbers look like perfect squares, check whether their square roots form a recognizable sequence.
Updated On: Jun 15, 2026
- 369
- 441
- 361
- 461
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
The series consists of squares of consecutive prime numbers.
Step 1: Express each term as a square. \[ 4=2^2 \] \[ 9=3^2 \] \[ 25=5^2 \] \[ 49=7^2 \] \[ 121=11^2 \] \[ 169=13^2 \] \[ 289=17^2 \]
Step 2: Find the next prime. After 17, the next prime number is 19. \[ 19^2=361 \] Hence the next term is \[ \boxed{361} \]
Step 1: Express each term as a square. \[ 4=2^2 \] \[ 9=3^2 \] \[ 25=5^2 \] \[ 49=7^2 \] \[ 121=11^2 \] \[ 169=13^2 \] \[ 289=17^2 \]
Step 2: Find the next prime. After 17, the next prime number is 19. \[ 19^2=361 \] Hence the next term is \[ \boxed{361} \]
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