设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6

设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6
设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.
S12-S6S改为S12-S6

设等比数列{an}的前n项和为sn,若S6,S9,S3成等差数列,问2S3,S6,S12-S6S能否成等比数列?请说明理由.S12-S6S改为S12-S6
因为S6,S9,S3成等差数列所以S6+S3=2S9,所以2a1(1+q+q^2)+a1q3(1+q+q^2)=2a(1+q+q^2+.q^8)解得q^3=-1 2S3*(S12-S6)=2a1(1+q+q^2)+aq^6(1+q+...q^5),把q^3=-1代入即可