已知等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437626481.png)
的首項
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437642371.png)
,公差
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437642443.png)
,等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437658491.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437673724.png)
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437626481.png)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437658491.png)
的通項公式;
(2)設(shè)數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437736450.png)
對任意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437751523.png)
均有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437767925.png)
,求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437736450.png)
的前n項和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437798388.png)
.
試題分析:(1)由已知可首先求得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437876416.png)
,進一步得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437814565.png)
;
根據(jù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437938781.png)
得到
(2)從
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437985603.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438001645.png)
①出發(fā),得到
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438016595.png)
,
再據(jù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437985603.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438048901.png)
②
①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438063165.png)
②,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438079768.png)
, 從而可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240504380941145.png)
,
從第二項起利用等比數(shù)列的求和公式.
(1)由題意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438110737.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438126491.png)
成等比數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438141716.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437642443.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437876416.png)
,
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438219675.png)
5分
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240504382501004.png)
, ①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438266767.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240504382821235.png)
, ②
①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438063165.png)
②得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438328945.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240504383601089.png)
10分
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438375357.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438391574.png)
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050438391435.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240504384062120.png)
所以,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824050437860511.png)
12分
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