设等比数列[an}的前n项和为Sn,S3+S6=2S9 则q=?
问题描述：
设等比数列[an}的前n项和为Sn,S3+S6=2S9 则q=?
答
a1(1-q^3)/(1-q)+a1(1-q^6)/(1-q)=2a1(1-q^9)/(1-q)
q^3+q^6=2q^9 q^3(2q^6-q^3-1)=0 (2q^3+1)(q^3-1)=0
2q^3+1=0 q=-(1/2)^(1/3)