Question

Let a_1, a_2, . . . , a_10 be an arithmetic sequence. If a_1 + a_3 + a_5 + a_7 + a_9 = 17 and a_2 + a_4 + a_6 + a_8 + a_{10} = 15, then find a_1.

Answer 1

5/2 (a + a+4*2d) = 17
5/2 (a+d + a+d+4*2d) = 15

a=5, d = -2/5

Check: The odd terms are
5, 21/5, 17/5, 13/5, 9/5. Sum=17
and I bet the evens add up as well.

Answer 2

Stop Cheating!

Answer 3

@AoPS Ur a cheater pretending to be an AoPS staff member