Question

等差数列log2a1+log2a2+...+log2a10=10

在各项为正数的等比数列{an}中,若a1乘a10=4 则log2a1+log2a2+...+log2a10=

Answer 1

因为是等比数列
a1*a10
=a1*a1*q^9
=a1^2q^9=4

a2*a9=a3*a8=a4*a7*a5*a6=4
log2a1+log2a2+...+log2a10
=log2 (a1*a2*a3*.a10)
=log2 (4*4*4*4*4)
=log2 2^10
=10