等比数列前n项和Sn,S6/S3=3,S9/S6=?

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等比数列前n项和Sn,S6/S3=3,S9/S6=?
等比数列前n项和Sn,S6/S3=3,S9/S6=?

等比数列前n项和Sn,S6/S3=3,S9/S6=?
S3=a1(1-q^3)/(1-q)
S6=a1(1-q^6)/(1-q)
S9=a1(1-q^9)/(1-q)
S6/S3=(1-q^6)/(1-q^3)=1+q^3=3
q^3=2
所以S9/S6=(1-q^9)/(1-q^6)=(1-8)/(1-4)=7/3

13/9

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