题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-61764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-13099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-17112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-94636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-36230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-85239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-30274.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-13099.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-13099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-18135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-92064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-96921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-22485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-94636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021506-99322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021506-24931.png)
(3)在满足(2)的条件下,求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021506-92276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-17112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-45117.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-59617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-20237.png)
解析
试题分析:(1)用公式
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-30863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-80609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-36230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-62892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-13099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-18135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-96271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-69535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-25462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-76354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-76354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-29761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021506-92276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021504-17112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-45117.png)
试题解析:(1)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-62035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-56416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021510-51473.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021510-80981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021510-25598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021510-95845.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021511-42746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021511-28698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021511-12958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021511-37383.png)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021503-13099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021512-54928.png)
(2)解:由(1)得,
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021505-18135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-96271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021512-88198.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-69535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021512-57658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021508-25462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021511-37383.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021509-76354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021512-63064.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021513-80262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-59617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021513-54579.png)
(3)解:由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-59617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021513-75549.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021513-79585.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021507-45117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021514-69510.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021514-67826.png)
②-①得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021514-24703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021514-29127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021514-78063.png)
核心考点
试题【设为数列的前项和,对任意的,都有为常数,且.(1)求证:数列是等比数列;(2)设数列的公比,数列满足,,求数列的通项公式;(3)在满足(2)的条件下,求数列的前】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021435-57445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021435-80392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021435-75346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021435-64351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021436-56111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021410-74819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021410-93186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021410-74819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021410-20959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021411-60502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021411-14338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021411-82258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021411-89592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-46349.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021410-74819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-64801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-15499.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-68908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-44675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021413-71521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021413-28432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021412-44675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021400-17565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021401-34672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021401-31786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021401-70700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021402-79857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021236-75391.png)
(1) 若数列{an}为等差数列,Sn是其前n项和,a3=4,S3=18,求Sn;
(2) 判断(1)中的数列{Sn}是否为“特界” 数列,并说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021035-97428.png)
(1)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009021035-52949.png)
(2)Sn+1=4an.
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