Question

1, 4, 9, 16, _______, 36, 49, 64

Answer 1

To identify the pattern and find the missing number in the sequence \(1, 4, 9, 16, \ldots, 36, 49, 64\), we first observe the numbers closely.

We can see that:
- \(1 = 1^2\)
- \(4 = 2^2\)
- \(9 = 3^2\)
- \(16 = 4^2\)

Following this pattern, the next term should be \(5^2\):
- \(25 = 5^2\)

Let's verify the rest of the sequence:
- \(36 = 6^2\)
- \(49 = 7^2\)
- \(64 = 8^2\)

So, the pattern is that each term in the sequence is a perfect square of consecutive integers starting from 1.

Therefore, the sequence \(1, 4, 9, 16, 25, 36, 49, 64\) is correct, and the missing number is \(25\).