Question

已知等差数列An中，公差d=1,求S98=137,a2+a4+a6+a8……a98的值

Answer 1

设S1=a2+a4+a6+......+a98,S2=a1+a3+a5......+a97,则S1+S2=137..................①
∵ d=1，∴S2=S1-49..................②
②带入①得S1=93.

Answer 2

S98 = [ (a1+a98) * 98 ] / 2 = 137
a1 + a98 + d = a2 + a98
可以解得 a2 + a98 = 186 / 49
a2 + a98 = a4 + a96 = a6 + a94 ……
可以求出，a2+a4+a6+a8……a98 = 186 / 49 / 2 *49 = 93