在等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项.已知数列a1,a2,ak1,ak2,...akn,...成等比数列,

题目

在等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项.已知数列a1,a2,ak1,ak2,...akn,...成等比数列,
求数列{Kn}的通项Kn

答案

由等差数列{an}中,若公差d≠0,a2是a1与a4的等比中项可知,a2*a2=a1*a4,
而a2=a1+d,a4=a1+3d,代入上式可得：a1=d；再由数列a1,a2,ak1,ak2,...akn,...成等比数列,可知：a2/a1=（a1+d）/a1=2a1/a1=2,即数列的公比为2,则数列{Kn}的通项Kn=a1*2^(n-1)