题目内容
[2014·湖北模拟]已知等比数列{an}中,各项都是正数,且a1,
a3,2a2成等差数列,则
=( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125918338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125934655.png)
A.1+![]() | B.1-![]() | C.3+2![]() | D.3-2![]() |
C
设等比数列{an}的公比为q(q>0),则由题意得a3=a1+2a2,即a1q2=a1+2a1q,q2-2q-1=0,解得q=1±
.又q>0,所以q=1+
,所以
=
=q2=(1+
)2=3+2
,选C.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125950344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125950344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125934655.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052126059846.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125950344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052125950344.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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A.1+![]() | B.1-![]() | C.3+2![]() | D.3-2![]() |