What is the sequence 2 9 5 13 10 19 17?

Answer 1

Look at the differences bettween the terms: 9-2=7, 5-9=-4, 13-5=8, 10-13=-3
The differences finally are: 7,-4,8-3,9,-2. The next difference must be 10, so the next term is 27(27-17=10) and the next difference must be -1, so the next term must be 26
(26-27=-1). Finally, the sequence is: 2 9 5 13 10 19 17 27 26 and so on.