The missing number in the sequence is 36.
This sequence consists of numbers that are perfect squares. Let’s analyze them:
- 1 is the square of 1 (1 x 1)
- 16 is the square of 4 (4 x 4)
- 100 is the square of 10 (10 x 10)
- 169 is the square of 13 (13 x 13)
Now, if we examine the integers whose squares are represented in the sequence, we see: 1, 4, 10, and 13. The gaps between these numbers suggest that 6 is the missing number, as it comes between 4 and 10. Thus, the square of 6 is 36 (6 x 6), which fits perfectly into the sequence.
Therefore, if we arrange the sequence including the missing number, it should be: 1, 16, 36, 100, 169.