题目内容
已知数列{
}是等差数列,且
=12,
=27,
①求数列{
}的通项公式; ②求数列{
}的前
项和![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344253388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344160348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344175314.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344191340.png)
①求数列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344160348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344222489.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344238297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344253388.png)
(1)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344253388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344300942.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232123442691141.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344253388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344300942.png)
(1)由
=12,
=27,可直接求出公差,然后利用
求出通项.
(2)由于数列{
}是等差数列,所以数列{
}要采用分组求和.
解:⑴∵数列{
}是等差数列,且
=12,
=27
∴数列{
}的公差
------------------
分
∴
--------------
分
⑵
…![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344893612.png)
…
…
---------
分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232123449871055.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344175314.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344191340.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344643760.png)
(2)由于数列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344160348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344222489.png)
解:⑴∵数列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344160348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344175314.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344191340.png)
∴数列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344160348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344799422.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344815287.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232123448461168.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344862290.png)
⑵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232123448771079.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344893612.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344909581.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344924789.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344940445.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344971291.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232123449871055.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212344300942.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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