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已知{an}为等差数列,且a1,a3,a6成等比,则(a2+a5)/(a4+a9)=?
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已知{an}为等差数列,且a1,a3,a6成等比,则(a2+a5)/(a4+a9)=?
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答案和解析
a3=a1+2d
a6=a1+5d
a1,a3,a6成等比
(a3)^2=a1*a6
(a1+2d)^2=a1(a1+5d)
a1=4d
(a2+a5)/(a4+a9)
=(a1+d+a1+4d)/(a1+3d+a1+8d)
=(2a1+5d)/(2a1+11d)
=(8d+5d)/(8d+11d)
=13/19
a6=a1+5d
a1,a3,a6成等比
(a3)^2=a1*a6
(a1+2d)^2=a1(a1+5d)
a1=4d
(a2+a5)/(a4+a9)
=(a1+d+a1+4d)/(a1+3d+a1+8d)
=(2a1+5d)/(2a1+11d)
=(8d+5d)/(8d+11d)
=13/19
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