The sequence is constructed as follows:
- 7 = 5 + 2
- 9 = 2 + 7
- 16 = 7 + 9
- 25 = 9 + 16
This pattern indicates that each number, starting from the third, is the sum of the two preceding numbers, analogous to the Fibonacci sequence. Consequently, the subsequent number in the series is:
\[
16 + 25 = 41.
\]