等差数列{an}中,an>0,且a1+a3+a8=a4^2,则S7=
问题描述：
等差数列{an}中,an>0,且a1+a3+a8=a4^2,则S7=
答
设数列公差为d.
a1+a3+a8=a4^2
3a1+9d=(a1+3d)^2
(a1+3d)^2-3(a1+3d)=0
(a1+3d)(a1+3d-3)=0
a1=-3d(an>0,a1>0,d>0 舍去)或a1+3d=3
S7=7a1+21d=7(a1+3d)=7×3=21