Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

booboo44 Aug 10, 2024

#1**+2 **

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*

threepointonefourone Aug 11, 2024