serrisha
幼苗
共回答了21个问题采纳率：76.2% 举报
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^2得：a1·q+a1·q^4=2a1·q^7 ,即a2+a5=2a8,故a2,a8,a5成等差数列.
1年前
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