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

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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)=0
q³=1或q³=-1/2,an的公比取q=-(1/2)^(1/3).

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