公差不为零的等差数列{an}的前n项和为Sn,若a4是a3与a7的等比中项,S10=60,S8等于?

问题描述:

公差不为零的等差数列{an}的前n项和为Sn,若a4是a3与a7的等比中项,S10=60,S8等于?

a4²=a3a7
(a1+3d)²=(a1+2d)(a1+6d)
-3d²=2a1d
a1=-3d/2
S10=10a+45d
=30d=60
d=2
a1=-3
S8=-3*8+56*2
=112-24
=88