等差数列an中,公差为d（不等于0）,且a1,a3,a9成等比数列,则（a1+a3+a9)/(a2+a4+a9)的值为

题目

等差数列an中,公差为d（不等于0）,且a1,a3,a9成等比数列,则（a1+a3+a9)/(a2+a4+a9)的值为

答案

a3=a1+2d
a9=a1+8d
a1a9=a3^2
a1*(a1+8d)=a1^2+8a1d
(a1+2d)^2=a1^2+4a1d+4d^2
a1^2+8a1d=a1^2+4a1d+4d^2
(a1-d)d=0
因为d不等于0
a1=d
（a1+a3+a9)/(a2+a4+a9)
=(a1+3a1+9a1)/(2a1+4a1+9a1)
=13a1/15a1
=13/15