设等差数列d不等于0,a1=9d若ak是a1与a2k的等比中项则k=

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设等差数列d不等于0,a1=9d若ak是a1与a2k的等比中项则k=

设等差数列d不等于0,a1=9d若ak是a1与a2k的等比中项则k=
设等差数列d不等于0,a1=9d若ak是a1与a2k的等比中项则k=

设等差数列d不等于0,a1=9d若ak是a1与a2k的等比中项则k=
a1=9d;
ak=a1+(k-1)d=(8+k)d;
同理a2k=(8+2k)d;
由题
[(8+k)d]^2=9d*(8+2k)d;
k1=4;
k2=-2

(ak)^2=a1·a2k
[9d+(k-1d)]^2=9d·[9d+(2k-1)d]
(k+8)^2=9(2k+8)
(k-4)(k+2)=0
k=4

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