设等差数列an的公差为d且d不等于0，且a1,a3,a9成等比数列，求a1*a2+a3*a4+a5*a6/a1a6+a2a5

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a1=a3-2d a9=a3+6d a1,a3,a9成等比数列 所以滑如凳a1*a9=（ a3）²橡数
即（a3-2d )*(a3+6d）= (a3）信旅² 化简得 a3=3d

于是an=nd
a1*a2+a3*a4+a5*a6=d*2d+3d*4d+5d*6d =44d²
a1a6+a2a5=d*6d+2d*5d=16d²

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a1,a3,a9成等比数列
a1*a9=a3*a3
(a1+2d)²=a1(a1+8d)
4d²+4a1d=8a1d
解得：a1=d
所以等差数者嫌运列an=nd
a1*a2+a3*a4+a5*a6/a1a6+a2a5
=（1*2+3*4+5*6）d²/（首梁1*6+2*5）d²者御
=44/16
11/4

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因为an为等差，a1，a3，a9为等比，议辩蠢档政数列为携乱a，2a，3a，档昌，，，，，9a，则答案为11/4

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