已知Sn是等比数列{an}的前n项和,已知S3,39,S6成等差数列,求证a2,a8,a5成等差数列.
问题描述：
已知Sn是等比数列{an}的前n项和,已知S3,39,S6成等差数列,求证a2,a8,a5成等差数列.
答
由等比数列求和公式知：S3=a1(1-q^3)/(1-q),S9=a1(1-q^9)/(1-q),S6=a1(1-q^6)/(1-q).所以,S3、S9、S6成等差数列即 a1(1-q^3)/(1-q)+a1(1-q^6)/(1-q)=2a1(1-q^9)/(1-q) 化简为 a1·q^3+a1·q^6=2a1·q^9 ,两边同除以q...