设等比数列{an}前n项的和为Sn,若S3+S6=2S9,求数列的公比q(要过程)
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设等比数列{an}前n项的和为Sn,若S3+S6=2S9,求数列的公比q(要过程)
设等比数列{an}前n项的和为Sn,若S3+S6=2S9,求数列的公比q(要过程)
设等比数列{an}前n项的和为Sn,若S3+S6=2S9,求数列的公比q(要过程)
当q=1,3a1+6a1=9a1=2*9a1不成立,所以q≠1
当q≠1时,a1(q^3-1)/(q-1)+a1(q^6-1)/(q-1)=2a1(q^9-1)/(q-1)
约去a1,(q-1),得q^3+q^6=2q^6
令q^3=t,原式t+t^2=2t^3
1+t=2t^2得t=-1/2
q^3=-1/2
q=开三方(-1/2)