+866 Let a_1, a_2, a_3, \dots be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_1 = \frac{1}{2}$ and $S_{2} = \frac{1}{2},$ then find $S_{15}.$
+208 If \(S_1\) is 1/2
that means \(a_1\) is 1/2.
If \(a_1 \) is 1/2, then \(a_2\) is 0
So \(a_{15}\) is 1/2 - 14(1/2) = 13/2
So 1/2 + 13/2 = 7
7 times 15/2 = 105/2
+208 If \(S_1\) is 1/2
that means \(a_1\) is 1/2.
If \(a_1 \) is 1/2, then \(a_2\) is 0
So \(a_{15}\) is 1/2 - 14(1/2) = 13/2
So 1/2 + 13/2 = 7
7 times 15/2 = 105/2
