已知数列是公差不为零的等差数列,且a1,a3,a9成等比数列,求(a1+a3+a9)/(a2+a4+a6)

问题描述:

已知数列是公差不为零的等差数列,且a1,a3,a9成等比数列,求(a1+a3+a9)/(a2+a4+a6)

答案为:12/11
a1,a3,a9成等比,所以,a3^2=a1*a9,即(a1+2d)^2=a1*(a1+8d),得:3a1=2d
(a1+a3+a9)/(a2+a4+a6)=(3a1+10d)/(3a1+9d)=12/11