设数列{an}是等差数列,公差d≠0,若ak,am,ap三个数成等比数列,则其公比为

题目

设数列{an}是等差数列,公差d≠0,若ak,am,ap三个数成等比数列,则其公比为
A.(m-p)/(k-p) B.(p-m)/(m-k) C.(m-k)/(m-p) D.(k-m)/(k-p)

答案

ap/am=am/ak
(ap-am)/am=(am-ak)/ak
am/ak=(ap-am)/(am-ak)=(p-m)d/((m-k)d)=(p-m)/(m-k)