高中《数学》(试验修订本·必修 )第一册(上 )第 132页例 4为“已知 Sn 是等比数列{ an}的前 n项和 ,S3 ,S9,S6成等差数列 ,求证a2 ,a8,a5成等差数列 .”本刊文 [1]将这道题推广为 :命题 1　已知 Sn 是等比数列 { an}的前 n项和 ,公比 q≠ 1,则 ak,ak+2 p,ak+p成等差数列的充要 High School “Mathematics” (Experimental Revisions, Revisions) Volume I (Top) Page 132 Example 4 is “The known Sn is the first n terms of the geometric series {an} and the S3, S9, and S6 are the arithmetic progressions. Prove that a2, a8, and a5 are equal arithmetic series.” This article [1] generalizes this question to: Proposition 1. Known Sn is the first n terms of {1}, and the common ratio q is 1. Ak, ak + 2 p, ak + p into a series of equal