The process of deriving the given terms is:
Start with 2.
Add 7 . . . . . 9
Minus 4. . . . 5
Add 8 . . . . . 13
Minus 3. . . . 10
Add 9 . . . . . 19
Minus 2. . . . 17
Next:
Add 10 . . . . 27
Minus 1. . . . 26
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27.
16 (add 3 every time).
The next number is 27. Nice puzzle! The reason is on discussion page, for those who are still working on it.
This is a peculiar number sequence which follows the following rule: +7, -4, +8, -3, +9, -2... The next few functions would be +10, -1, +11, -0 And thus the next few numbers in the sequence would be 17+10=27, 27-1=26, and so on. The sequence in total goes 2, 9, 5, 13, 10, 19, 17, 27, 26, 37, 37.
27