题目内容
已知
满足
,
,
(1)求
;
(2)求证:
是等比数列;并求出
的表达式.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558356473.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558372423.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558388576.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558403565.png)
(2)求证:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558419556.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558434347.png)
(1)
7,![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558481826.png)
(2)见解析
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558450367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558481826.png)
(2)见解析
(1)
,
同理,![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558481826.png)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240505585281051.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240505585441333.png)
又![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558575564.png)
所以数列
是以4为首项,2为公比的等比数列
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558606751.png)
,
点评:本题属于容易题,主要考查了递推公式的应用以及等比数列的定义和通项公式的求法。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558497769.png)
同理,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558481826.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240505585281051.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240505585441333.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558575564.png)
所以数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558419556.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558606751.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558622564.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050558637674.png)
点评:本题属于容易题,主要考查了递推公式的应用以及等比数列的定义和通项公式的求法。
![](http://thumb.zyjl.cn/images/loading.gif)
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