设等差数列{an}的公差d不为0,a1=9d.若ak是a1与a2k的等比中项,则k=(  ) A.2 B.4 C.6 D.8

问题描述:

设等差数列{an}的公差d不为0,a1=9d.若ak是a1与a2k的等比中项,则k=(  )
A. 2
B. 4
C. 6
D. 8

因为ak是a1与a2k的等比中项,
则ak2=a1a2k,[9d+(k-1)d]2=9d•[9d+(2k-1)d],
又d≠0,则k2-2k-8=0,k=4或k=-2(舍去).
故选B.