已知等比数列{an}满足an>0(n∈N*),且a5a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+log2a5+…+log2a2n-1等于()A.(n+1)2B.n2C

题目简介

已知等比数列{an}满足an>0(n∈N*),且a5a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+log2a5+…+log2a2n-1等于()A.(n+1)2B.n2C

题目详情

已知等比数列{an}满足an>0(n∈N*),且a5a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+log2a5+…+log2a2n-1等于(  )
A.(n+1)2B.n2
C.n(2n-1)D.(n-1)2
题型:单选题难度:中档来源:不详

答案

B
由等比数列的性质可知a5a2n-5=,
又a5a2n-5=22n,所以an=2n.
又log2a2n-1=log222n-1=2n-1,
所以log2a1+log2a3+log2a5+…+log2a2n-1=1+3+5+…+(2n-1)= =n2,故选B.

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