+713 Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.
+130440 Let a1 be the first term and d the common difference between rwems
5a1 + 4d = 1/5 (mult through by -2) → -10a1 -8d = -2/5 (1)
10a1 + 9d = 1/10 (2)
Add (1) , (2)
d = -3/10
5a1 - 4(3/10) = 1/5
5a1 -12/10 = 1/5
5a1 - 6/5 = 1/5
5a1 = 7/5
a1 = 7/35
S15 = 15a + 14d = 15(7/35) + 14 (-3/10) = -6/5
