Complete this sequence 2 9 5 13 10 19 17?

Answer 1

It continues: 2, 9, 5, 13, 10, 19, 17, 27, 26, 37, 37, 49, 50, 63, 65, 79, 82, ...

The sequence consists of terms taken alternately from 2 sequences:

1. 2, 5, 10, 17, 26, 37, 50, 65, 82, ... which starts at 2 and the difference between each term increases by 2, starting with a difference of 3;
2. 9, 13, 19, 27, 37, 49, 63, 79, ... which starts at 9 and the difference between each term increases by 2, starting with a difference of 4.

Together these provide a sequence where the difference between the terms alternates between two sequences that increase by 1 each time: one sequence is +7, +8, +9, +10, +11, +12, +13, ... and the other is -4, -3, -2, -1, 0, +1, +2, ..., ie the differences between the terms are +7, -4, +8, -3, +9, -2, +10, -1, +11, 0, +12, +1, +13, +2, ...