一个公差不为0的等差数列an中,a1a5a17成等比数列,则其公比为

问题描述:

一个公差不为0的等差数列an中,a1a5a17成等比数列,则其公比为

a5=a1+4d
a17=a1+16d
(a5)^2=a1*a17
(a1+4d)^2=a1*(a1+16d)
(a1)^2+16d^2+8da1=(a1)^2+16da1
16d^2=8da1 a1=2dd=a1/2
所以a1=a1a5=3a1 a17=a1+16d=9a1 所以q=3