Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$
0 + 55d = 1/5
55d = 1/5
d = 1 / [ 5 * 55] = 1 / 275
70th term is 0 + 60d = 60 / 275 =12 / 55
S70 = [ 12/55 + 0 ] [70 -10 + 1 ] / 2 =
[12/55] * 61 / 2 =
366 / 55
+910 
