已知Sn是等比数列{An}的前N项和,S3,S9,S6成等差数列,则

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已知Sn是等比数列{An}的前N项和,S3,S9,S6成等差数列,则
A .A3+A6=A9
B.A3*A6=A9
C.A3+A6=2A9
D.A3*A6=A9^2
求详解

由题意,
S9-S3=S6-S9
而
S9-S3=A4+...+A9
S6-S9=-(A7+A8+A9)
而(A4+A5+A6)+2(A7+A8+A9)=0
A3(Q+Q²+Q²)+2A6(Q+Q²+Q²)=0
A3=-2A6
所以A6=-2A9
A3=4A9
故A3+A6=2A9

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