Let a_1, a_2, a_3, \dots be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S1=12 and S2=12, then find S15.
If S1 is 1/2
that means a1 is 1/2.
If a1 is 1/2, then a2 is 0
So a15 is 1/2 - 14(1/2) = 13/2
So 1/2 + 13/2 = 7
7 times 15/2 = 105/2
If S1 is 1/2
that means a1 is 1/2.
If a1 is 1/2, then a2 is 0
So a15 is 1/2 - 14(1/2) = 13/2
So 1/2 + 13/2 = 7
7 times 15/2 = 105/2