设等比数列{an}中,a3是a1,a2的等差中项,则数列的公比为_.
问题描述:
设等比数列{an}中,a3是a1,a2的等差中项,则数列的公比为______.
答
设等比数列{an}的公比为q,
则:a2=a1q,a3=a1q2,
由a3是a1,a2的等差中项,
得:2a3=a1+a2,即2a1q2=a1+a1q,
因为a1≠0,所以2q2-q-1=0,解得:q=−
或q=1.1 2
故答案为−
或1.1 2