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
答
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.