题目
题型:不详难度:来源:
在等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080316-63266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080317-71709.png)
(Ⅰ)求通项
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080317-73409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-93614.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-93614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-86673.png)
(Ⅲ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-42136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-58672.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-21526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-61101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-49748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-15730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-86533.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-34199.png)
解析
试题分析:(Ⅰ)设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080316-63266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-22701.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080317-71709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-52274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-30092.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-73126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080321-35798.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080321-73791.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080321-60107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080319-49748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080321-39320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080321-33693.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-27783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-66376.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-14469.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-91258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-58672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-39831.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080323-50011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-58672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080323-85436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080323-37392.png)
综上所述,数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-42136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080320-34199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-86673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-86673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080318-86673.png)
点评:本题第(Ⅱ)问也可以令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080323-72307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080322-91258.png)
核心考点
举一反三
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080234-81633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080235-88310.png)
(Ⅰ)证明:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080235-13451.png)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080234-81633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080235-89849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080235-44137.png)
(Ⅲ)如果对任意的正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080235-40510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080236-10337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080247-76611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080228-18904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080228-92421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080228-18904.png)
A.128 | B.80 | C.64 | D.56 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080221-14547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080222-57736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080215-27724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080215-73404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080216-43861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080216-91865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080210-95457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080210-72636.png)
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