+1364 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 $S_{70}.$
+129850 Let the first term = S1 and the common difference = d
Sum of first n terms = n *S1 + [ (n -1) (n) / 2 ] d
S20 = 20S1 + 190 d = 1/5 (1)
S10 = 10S1 + 45d = 0 (2)
Multiply (1) by -2
-20S1 - 90d = 0 add this to (1)
100d = 1/5
d = 1/500
10S1 + (45)(1/500) = 0
10S1 = -45 / 500 = -9/100
10S1 = -9/100
S1 = -9 / 1000
S70 = 70S1 + 2415d = 70 (-9/1000) + 2415 (1/500) = 21 / 5
