Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_1 = \frac{1}{5}$ and $S_2 = \frac{1}{10},$ then find $S_{15}.$
S1 = a1 = 1/5
S2 = 2a1 + d
1/10 = 2/5 + d
1/10 - 2/5 = d
d = -3/10
sum of the first n terms of an arithmetic sequence =
(n)*a1 + (n)(n-1)/2 *d
S15 = (15 ) (1/5) + (15)(14)/2 * (-3/10) = 3 - 63/2 = -57/2 = - 28.5
+153 
