Break into two sub-sequences taking every other term:
5,10, 3,6,-1,-2,-9 <--original sequence
5, 3, -1, -9 <--first sub-sequence
10, 6, -2, <--second sub-sequence
First sequence: 5,3,-1,-9,...
5 <--start with 5
5 - 2 = 3
3 - 4 = -1
-1 - 8 = -9 so we continue the pattern of doubling what we subtract
-9 - 16 = -25
-25 - 32 = -57
Second sequence: 10,6,-2,...
10 <-- start with 10
10 - 4 = 6
6 - 8 = -2 so we continue the pattern of doubling what we subtract
-2 - 16 = -18
-18 - 32 = -50
-50 - 64 = -114
5, 3, -1, -9, -25, -57 <--first sub-sequence
10, 6, -2, -18, -50 -114 <--second sub-sequence
5,10, 3,6,-1,-2,-9,-18,-25,-50,-57,-114 <---original sequence
That's 5 more terms. You only wanted 3.
Edwin
