next 27
alternating >
2 5 10 17 = +3 +5 +7 so next is +9 (add 2 each time)
9 13 19 = +4 +6 so next is +8 (add 2 each time)
2 5 10 17 26 37 50 65 82 101 ...
9 13 19 27 37 49 63 79 97 117 ...
becoming
2 9 5 13 10 19 17 27 26 37 37 49 50 63 65 79 82 97 101 117 ...
27.
The next figure would be 21, followed by 11 & 10.
22
18. The pattern is add 5, then subtract 1.
The next number in the sequence is 27.
It's, 7n+6
18
37.
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.
20
The next number is 27. Nice puzzle! The reason is on discussion page, for those who are still working on it.
119. un = (-n4 + 15n3 - 77n2 + 225n + 192)/6