等差数列AN中,公差D不等于0.且A1,A3,A9成等比数列则(a1+a3+a5)/(a2+a4+a6)的值为?

问题描述:

等差数列AN中,公差D不等于0.且A1,A3,A9成等比数列则(a1+a3+a5)/(a2+a4+a6)的值为?

(a1+a3+a5)/(a2+a4+a6)=(3a1+6d)/(3a1+9d)
a3^2=a1*a9,则(a1+2d)^2=a1*(a1+8d),所以4a1*d+4d^2=8a1*d,故a1=d
(a1+a3+a5)/(a2+a4+a6)=(3a1+6d)/(3a1+9d)=9d/12d=3/4