在等比数列an中,a5=16,则log2a1+log2a2+.+log2a9=

题目

在等比数列an中,a5=16,则log2a1+log2a2+.+log2a9=

答案

设数列公比为q.
a5=a1q^4=16
log2(a1)+log2(a2)+...+log2(a9)
=log2(a1a2...a9)
=log2(a1^9q^36)
=log2[(a1q^4)^9]
=9log2(a1q^4)
=9log2(16)
=9×4
=36