The next number in the sequence: 1, 9, 25,57 … is

The next number in the sequence: 1, 9, 25,57 … is
A 121
B: 36
C: 64
D: 81

The correct answer and explanation is:

The correct answer is D: 81.

Explanation:

This sequence follows a pattern based on the square of consecutive integers. Let’s break it down:

1. The first number in the sequence is 1. This is the square of 1 (1² = 1).
2. The second number is 9. This is the square of 3 (3² = 9).
3. The third number is 25. This is the square of 5 (5² = 25).
4. The fourth number is 57. This is the square of 7 (7² = 49), but there is a pattern here: it seems that after squaring, we add an incrementally increasing number to each result.
   • 1² + 0 = 1
   • 3² + 0 = 9
   • 5² + 0 = 25
   • 7² + 8 = 57

The next number in the sequence should follow this pattern. After 7, the next integer to square is 9, and the addition follows the same trend of adding a slightly larger number, this time 24.

So, we compute:

• 9² = 81
• 81 + 0 (following the pattern) = 81

Thus, the next number in the sequence is 81.