设等差数列{an}的公差为d不为0,a1=9d,若ak是a1与a2k的等比中项,则k=

问题描述:

设等差数列{an}的公差为d不为0,a1=9d,若ak是a1与a2k的等比中项,则k=

a1=9d
ak=a1+(k-1)*d=9d+(k-1)*d
a2k=a1+(2k-1)*d=9d+(2k-1)*d
ak^2=a1*a2k
化简后可求出k=4