+990 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 $a_1$.
+3311
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 $a_1$.
a1 = a1
a2 = a1 + d
a3 = a2 + d = (a1 + d) + d = a1 + 2d
a4 = a3 + d = (a1 + 2d) + d = a1 + 3d etc.
a2 + a4 = (a1 + d) + (a1 + 3d) = 2a1 + 4d = 6
a1 + a3 = (a1) + (a1 + 2d) = 2a1 + 2d = 5
by subtraction 2d = 1
d = 0.5
2a1 + 4d = 6
2a1 + (4)(0.5) = 6
2a1 = 6 – 2 = 4
a1 = 2
.
