The missing number in the series is 2401.
Let’s break down the series first:
- 1 is 12
- 16 is 42
- 81 is 92
- 625 is 252
- 1296 is 362
Now, let’s identify the numbers that are squared:
- 1 = 12
- 4 = 22
- 9 = 32
- 25 = 52
- 36 = 62
If we look closely, we see that the sequence of numbers whose squares appear in the series is 1, 4, 9, 25, 36. The missing number is related to 72.
The square of 7 is 49, which means the next entry in our series should be 492 = 2401.
Therefore, the complete sequence is 1, 16, 81, 625, 2401, 1296.