+513 Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.
+129820 a1 + a3 = 5
a2 + a4 = 6
a2 = a1 + d
a3 = a1 + 2d
a4 = a1 + 3d where d = the difference in successive terms....so....
a1 + (a1 + d) = 5
(a1 + d) + (a1 + 3d) = 6 simplify these
2a1 + d = 5 (1)
2a1 + 4d = 6 (2)
Subtract (1) from (2)
3d = 1
d =1/3
Using (1)
2a1 + (1/3) = 5
2a1 = 14/3
a1 = 14 / 6 = 7 / 3
