题目
题型:不详难度:来源:
(1)求数列{an}的通项公式an及前n项和Sn;
(2)若数列{bn}满足
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163026-25129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163026-39026.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163026-29088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-92099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-51397.png)
解析
试题分析:(1)设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-30719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-86688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-69579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-86688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-96576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-81360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-37381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-80814.png)
(2)根据(1)中的
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-81360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163029-78878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163029-63848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163029-40091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163026-39026.png)
试题解析:(1)解:设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-30719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-86688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163029-75347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163030-10087.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163036-35751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163028-96576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163036-52331.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163036-40922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163037-55526.png)
由①②解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163037-12864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163037-74605.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163026-29088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163027-92099.png)
(2)解:由(1)知:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163037-67721.png)
累加,得:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163037-31353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163038-14984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163038-93549.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163038-44230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163038-86520.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163038-54379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163039-84011.png)
核心考点
试题【已知各项都不相等的等差数列{an}的前六项和为60,且a6为a1和a21 的等比中项.(1)求数列{an}的通项公式an及前n项和Sn;(2)若数列{bn}满足】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
(1)求数列{an}的通项公式;
(2)在an与an + 1之间插入n个数,使这n + 2个数组成一个公差为dn的等差数列.
①在数列{dn}中是否存在三项dm,dk,dp (其中m,k,p成等差数列)成等比数列?若存在,求出这样的三项,若不存在,说明理由;
②求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011163002-30662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162826-60328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162826-25321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162826-17862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162712-40835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162713-29775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162713-60533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162713-43682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162713-22194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162714-28488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162714-40379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162714-35827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162713-22194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162714-40379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162714-28488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162703-99041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162703-88866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-13995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-56205.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-38749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-31776.png)
(2)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-31776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-13995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162705-27740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162705-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162705-93876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162704-31776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162633-12529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162634-63295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162634-63547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162634-77289.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162634-50197.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162633-12529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162634-58626.png)
(3)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162635-40803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162635-47221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162635-59860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162636-14874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162635-47221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011162636-20175.png)
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