已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243876471.png)
是等差數(shù)列,前n項(xiàng)和是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243891388.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243907532.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243922551.png)
,
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243876471.png)
的通項(xiàng)公式;
(2)令
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243954365.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243954347.png)
·2
n,求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243969487.png)
的前n項(xiàng)和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243985374.png)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244000469.png)
,(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244016707.png)
試題分析:(1)等差數(shù)列的求解方法為待定系數(shù)法,利用已知兩個(gè)條件,列出關(guān)于首項(xiàng)及公差的方程組
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240352440321286.png)
,解出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244047659.png)
,從而可得數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035243876471.png)
的通項(xiàng)公式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244000469.png)
;(2)數(shù)列求和,要先分析通項(xiàng)特征,本題是等差乘等比型,因此應(yīng)用錯(cuò)位相減法求和. 設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244078874.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244094984.png)
,錯(cuò)位相減得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244110907.png)
,再利用等比數(shù)列求和公式化簡得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240352441251675.png)
試題解析:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244141169.png)
解:(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244156933.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244172223.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244047659.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244000469.png)
4分
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244234586.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244078874.png)
①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244094984.png)
② 6分
① ②
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824035244110907.png)
8分
所以:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240352442971671.png)
12分
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