Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.
a3 = a1 + 2d
a2 = a1 + d
a4 = a1 + 3d
a6 = a1 + 5d
So we have these equations
a1 + a1 + 2d = -2
a1 +d + a1 + 3d + a1 + 5d = 1 simplify
2a1 + d = -2
3a1 + 9d = 1
Multiply the first equation by -9 and add to the second
-15a1 = 19
a1 = -19 / 15
+219 
