The sum of the first n terms of the arithmetic sequence {an} is SN. Given am − 1 + am + 1 − A2M = 0, s2m-1 = 38, then M = () A. 9B. 10C. 20D. 38

The sum of the first n terms of the arithmetic sequence {an} is SN. Given am − 1 + am + 1 − A2M = 0, s2m-1 = 38, then M = () A. 9B. 10C. 20D. 38

According to the property of arithmetic sequence, we can get: am-1 + am + 1 = 2am, then am-1 + am + 1-am2 = am (2-AM) = 0, the solution is: am = 0 or am = 2, and s2m-1 = (2m − 1) (a1 + A2M − 1) 2 = (2m-1) am, if am = 0, obviously (2m-1) am = 38 does not hold, so there should be am = 2, then s2m-1 = (2m-1) am = 4M-2 = 38