{an}是公差为-2的等差数列,a1+a4+a7+.+a28=90,求a4+a6+a8+.+a22?

题目

{an}是公差为-2的等差数列,a1+a4+a7+.+a28=90,求a4+a6+a8+.+a22?

答案

a1+a4+a7+.+a28=90
(a1+a28)*10/2=90
a1+a28=18
a28=a1+27d=a1-54
a1=36.
a4=a1+3d=36-6=30
a22=a1+21d=36-42=-6
a4+a6+a8+.+a22
=(a4+a22)*10/2
=120