题目内容
已知
,数列
的前
项和![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050308773.gif)
(1)求数列
的通项公式;
(2)若
,
,求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050261716.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050277522.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050292192.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050308773.gif)
(1)求数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050339267.gif)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050339719.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050386381.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050401674.gif)
()
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050417580.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050433709.gif)
(1)解:∵ ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050448598.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050464128.gif)
时
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050511565.gif)
亦即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050620566.gif)
故
是公差为
,首项
的等差数列———2分
∴
,即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050760573.gif)
当
时,
——4分
当
时,
亦适合
∴
———5分
(2)(理)解:
∵
———6分
———8分
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134051025553.gif)
———9分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134051119604.gif)
——(10分)
∴
———12
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050448598.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050464128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050479249.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050495757.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050511565.gif)
亦即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050620566.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050667419.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050698225.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050729532.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050745723.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050760573.gif)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050479249.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050807786.gif)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050869232.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050885252.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050901422.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134050417580.gif)
(2)(理)解:
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231340509942049.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231340510101659.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134051025553.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231340510881139.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134051119604.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134051135463.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231340511501076.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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