Question

已知公差不为0的等差数列{an}中,a1、a3、a4成等比数列，Sn是{an}的前n项和,则(S3-S2)/(S5-S3)=?

祥解

Answer 1

a1,a3,a4成等比数列,(a1+2d)/a1=(a1+3d)/(a1+2d)
2d/a1+1=1+d/(a1+2d)
d不＝0．
有：2a1+4d=a1
a1=-4d

则(S3-S2)/ (S5-S3)
=a3/(a5+a4)
=(a1+2d)/(a1+4d+a1+3d)
=(2d-4d)/(4d-4d-4d+3d)
=-2d/-d
=2