+556 Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.
+42 Let a1 be the first term
Let d be the difference between each term (that is, a2 - a1, or a3 - a2, etc)
a1 + (a1 + 2d) = -2
(a1 + d) + (a1 + 3d) + (a1 + 5d) = 1
Simplify first equation:
2a1 + 2d = -2
a1 + d = -2
Wait what? we see a1 + d = a2 = -2 !!!
Simplify second equation
-2 + (2a1 + 8d) = 1
2a1 + 8d = 3
minus 2(a1 + d) = 2(-2)
6d = 3 - (-4)
d = 6/7
since a2 = -2,
d = -2 - 6/7 = -2 6/7 = -20/7
