设Sn是等比数列的前n项和,若S3,S9,S6成等差数列,这an的公比q为多少
问题描述：
设Sn是等比数列的前n项和,若S3,S9,S6成等差数列,这an的公比q为多少
答
S3=a1(1-q³)/(1-q),S9=a1(1-q^9)/(1-q),S6=a1(1-q^6)/(1-q),2S9=S3+S6,2a1(1-q^9)/(1-q)=a1(1-q³)/(1-q)+a1(1-q^6)/(1-q),2q^9=q³+q^6,2q^6=1+q³,(q³-1)(2q³+1)=0q³=1或q³=...