Step-by-step Solution:

In this series: **16, 33, 65, 131, 261...**
The pattern followed is:
Multiply each number by 2, then alternately add 1 and subtract 1.
- \( (16 \times 2) + 1 = 33 \)
- \( (33 \times 2) - 1 = 65 \)
- \( (65 \times 2) + 1 = 131 \)
- \( (131 \times 2) - 1 = 261 \)
- \( (261 \times 2) + 1 = 523 \)