设{an}是正项等差数列,{bn}是正项等比数列,且a1=b1,a2n+1=b2n+1则()A.an+1=bn+1B.an+1≥bn+1C.an+1≤bn+1D.an+1<bn+1-数学

题目简介

设{an}是正项等差数列,{bn}是正项等比数列,且a1=b1,a2n+1=b2n+1则()A.an+1=bn+1B.an+1≥bn+1C.an+1≤bn+1D.an+1<bn+1-数学

题目详情

设{an}是正项等差数列,{bn}是正项等比数列,且a1=b1,a2n+1=b2n+1则(  )
A.an+1=bn+1B.an+1≥bn+1C.an+1≤bn+1D.an+1<bn+1
题型:单选题难度:中档来源:不详

答案

∵{an}是正项等差数列,{bn}是正项等比数列,且a1=b1,a2n+1=b2n+1 .
∴an+1 =
a1+a2n+1
2
,b2n+1 =
b1•b2n+1
=
a1•a2n+1

∵由基本不等式可得  
a1+a2n+1
2
a1•a2n+1
,当且仅当 a1=a2n+1时,等号成立.
故有an+1≥bn+1,
故选B.

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