等比数列{an}中,a4+a6=3,则a5(a3+2a5+a7)=_.

问题描述:

等比数列{an}中,a4+a6=3,则a5(a3+2a5+a7)=______.

设等比数列的公比为q,
因为a4+a6=3,所以a1q3(1+q2)=3,
a5(a3+2a5+a7)=a12q6(1+2q2+q4)=[a1q3(1+q2)]2=32=9.
故答案为:9.