已知等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列求证A2,A8,A5成等比数列

已知等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列求证A2,A8,A5成等比数列
已知等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列
求证A2,A8,A5成等比数列

已知等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列求证A2,A8,A5成等比数列
因为S3.S9.S6成等差数列
2S9=S3+S6
2a1(1-q^8)/(1-q)=a1(1-q^2)/(1-q)+a1(1-q^5)/(1-q)
2(1-q^8)=2-q^2-q^5
2q^8=q^2+q^5
2q^7=q+q^4
2a1q^7=a1q+a1q^4
2a8=a2+a5
所以a2.a8.a5成等差数列