PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
36
Explanation
This number series consists of the squares of consecutive natural numbers. For example: \( 1^2 = 1 \), \( 2^2 = 4 \), \( 3^2 = 9 \), \( 4^2 = 16 \), \( 5^2 = 25 \). The formula for the sequence is \( n^2 \). Therefore, the next number after 25 will be the square of 6, which is \( 6^2 = 36 \).
Key Points
- > This is a classic 'Perfect Squares' series.
- > Alternative logic: Addition of consecutive odd numbers: 1+3=4, 4+5=9, 9+7=16, 16+9=25.
- > Next would be 25 + 11 = 36.
- > Memorizing squares up to 20 is crucial for competitive reasoning.
- > \( 7^2 = 49 \), \( 8^2 = 64 \), \( 9^2 = 81 \), \( 10^2 = 100 \).
- > A perfect cubes sequence would be: 1, 8, 27, 64, 125.
Additional Information
Square Sequence Breakdown
| Position (n) | Formula | Value |
|---|---|---|
| 1 | \( 1^2 \) | 1 |
| 2 | \( 2^2 \) | 4 |
| 5 | \( 5^2 \) | 25 |
| 6 | \( 6^2 \) | 36 |
Memory Tips
- Odd Jumps: Look at the gaps if you forget squares: +3, +5, +7, +9. The next jump must be +11 (25 + 11 = 36).