已知等比数列{an}满足an>0,n∈N*,且a5·a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+…+log2a2n-1=()A.n(2n-1)B.(n+1)2C.n2

题目简介

已知等比数列{an}满足an>0,n∈N*,且a5·a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+…+log2a2n-1=()A.n(2n-1)B.(n+1)2C.n2

题目详情

已知等比数列{an}满足an>0,n∈N*,且a5·a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+…+log2a2n-1=(  )
A.n(2n-1)B.(n+1)2C.n2D.(n-1)2
题型:单选题难度:中档来源:不详

答案

C
设等比数列{an}的公比为q,∵a5·a2n-5=22n(n≥3),∴a1q4·a1q2n-6=22n,即a12·q2n-2=22n⇒(a1·qn-1)2=22n⇒(an)2=(2n)2,∵an>0,∴an=2n,∴a2n-1=22n-1,∴log2a1+log2a3+…+log2a2n-1=log22+log223+…+log222n-1=1+3+…+(2n-1)=·n=n2.

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