The next number in the sequence is 125.
To explain why, let’s take a closer look at how the sequence is formed.
The given sequence is: 5, 13, 29, 61.
If we analyze the differences between each pair of successive numbers, we get:
- 13 – 5 = 8
- 29 – 13 = 16
- 61 – 29 = 32
Now, if we look at those differences: 8, 16, 32, we can see that each difference is double the previous one. So, the differences seem to follow a pattern where each term is multiplied by 2:
- 8 (which is 23)
- 16 (which is 24)
- 32 (which is 25)
Following this pattern, the next difference should be:
32 * 2 = 64.
So, to find the next term in the sequence, we add this difference to the last term:
61 + 64 = 125.
Thus, the next number in the sequence is 125.