+280 Let \(a_1, a_2, a_3, \dots, a_{10}, a_{11}, a_{12}\) be an arithmetic sequence. If \(a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = -2\) and \(a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 1\), then find \(a_1\).
+129845 a2 + a4 + a6 + a8 + a10 + a12 = 1
a1 + a3 + a5 + a7 + a9 + a11 = -2 subtract these and we get
Note : an - an -1 = d
d + d + d + d + d + d= 3
6d =3
d = 1/2
Sum of terms from a1 to an = n * a1 + (n)(n-1) / 2 * d
S12 =
12a1 + 66d = 3
12a1 + 66 (1/2) = 3
12a1 + 33 = 3
12a1 = -30
a1 = -30 / 12 = - 5/2
