Understanding the Sequence
To find the missing numbers in the sequence 2, 3, 5, 9, 17, _, _, _, we first need to identify a pattern.

Identifying Patterns
- Let's look at the differences between consecutive terms:
- 3 - 2 = 1
- 5 - 3 = 2
- 9 - 5 = 4
- 17 - 9 = 8
- The differences are: 1, 2, 4, 8.

Recognizing the Pattern
- Notice that these differences (1, 2, 4, 8) are powers of 2:
- 2^0 = 1
- 2^1 = 2
- 2^2 = 4
- 2^3 = 8
- This suggests that the next difference should be 2^4 = 16.

Calculating the Next Terms
- Adding the next difference (16) to the last known term (17):
- 17 + 16 = 33
- The next term is 33.

Continuing the Sequence
- Continuing this pattern, the next difference would be 2^5 = 32:
- 33 + 32 = 65
- Next difference would be 2^6 = 64:
- 65 + 64 = 129

Final Sequence
- The complete sequence is: 2, 3, 5, 9, 17, 33, 65, 129.
- Hence, the missing numbers are **33, 65, and 129**.