Question

在等比数列an中,a1.a2.a3.a4=1,a13.a14.a15.a16=8,则a41.a42.a43.a44=

Answer 1

设等比数列的公比为q,则：

a13=a1*q^12；a14=a2*q^12；……

所以,a13*a14*a15*a16=a1*a2*a3*a4*q^48

===> 8=1*q^48

===> q^48=8

而,a41=a1*q^40；a42=a2*q^40……

所以,a41*a42*a43*a44=a1*a2*a3*a4*q^160=1*q^160=(q^48)^(10/3)

=8^(10/3)

=(2^3)^(10/3)

=2^10

=1024