Question

已知等比数列{an}中,a1=2,Sn是{an}的前n项和,若S9是S3和S6的等差中项,则a7=

Answer 1

等比数列{an}；设公比为q;

S9=a1*(1-q^9)/(1-q);

S3=a1(1-q^3)/(1-q);

S6=a1(1-q^6)/(1-q)

若S9是S3和S6的等差中项:

所以q0)Sn单调递增；S9>S3>S6;2S9>S3+S6

2S9=S3+S6;

因为q0舍去）q^3=-1/2;

a7=a1*q^6=2*(q^3)^2=2*(-1/2)^2=1/2