题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-77333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-14382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-13304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-14202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-78868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-76892.png)
(Ⅰ)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-87818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-77333.png)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074356-39297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074357-40277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-14382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074356-39297.png)
(Ⅲ)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-21480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-86256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-32678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-21480.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-66849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-81917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-98584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-97060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-93379.png)
解析
试题分析:(Ⅰ)由已知得,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-66849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-81917.png)
由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-78868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-88181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-11043.png)
两式相减,得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-98907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-88181.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-14202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-66849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-44817.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-77333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074405-60958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074405-23007.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-77333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-98584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-76892.png)
(Ⅱ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074405-18598.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074405-45390.png)
两式相减得,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074406-69592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074403-97060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-76892.png)
(Ⅲ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-88181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074406-83250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074406-42218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074406-45931.png)
相加得,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074407-41532.png)
依题意
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074407-99004.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-86256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074407-23265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-88181.png)
显然当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074402-86256.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074404-93379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074345-76892.png)
点评:本题主要涉及到的是由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074344-13304.png)
核心考点
试题【(本小题满分12分)设数列的前项和为.已知,,.(Ⅰ)写出的值,并求数列的通项公式;(Ⅱ)记为数列的前项和,求; (Ⅲ)若数列满足,,求数列的通项公式。】;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/20191012/20191012074327-60418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074327-48927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074328-88299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074328-33102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074328-36871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074328-13994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074329-42771.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074327-60418.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074329-18262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074329-61087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074329-95578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074327-48927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074329-61087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074318-92376.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074318-38876.png)
A.15 | B.30 | C.31 | D.64 |
A.33 | B.72 | C.84 | D.189 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074302-61852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074302-26559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012074302-38494.png)
A.–4 | B.–6 | C.–8 | D.–10 |
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