若等差数列｛an｝的公差d≠0,且a1,a5,a10成等比数列,则此等比数列的公比q=?

题目

若等差数列｛an｝的公差d≠0,且a1,a5,a10成等比数列,则此等比数列的公比q=?

答案

(a5)^2=a1*a10
(a1+4d)^2=a1*(a1+9d)
16d^2=da1
16d=a1
q=a5/a1
=(a1+4d)/a1
=(16d+4d)/(16d)
=5/4