题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-87866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-69931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-95028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-59344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-20601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-87866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-90844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-35059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-86068.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-87866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-69931.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-87216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-90844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105750-38930.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105750-87745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105750-14700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-79044.png)
解析
试题分析:本题考查等差数列与等比数列的概念、通项公式、前n项和公式、数列求和等基础知识,考查运算能力和推理论证能力.第一问,将已知条件中的
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-90844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-39487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-38523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-84857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-28758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105752-15884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105749-90844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105752-16451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105752-41659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105753-92393.png)
试题解析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105753-23560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105753-85561.png)
两式作差得:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105753-14686.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105754-48001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105748-87866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105754-18070.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105754-65038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105754-85836.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105750-87745.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105755-27937.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105755-59850.png)
两式相减得:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105755-42875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105755-15803.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105756-29782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105750-14700.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105756-37904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105756-65147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105756-40383.png)
两式作差得:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105757-28748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105757-90206.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105751-79044.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105730-96932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105730-62772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105730-96932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105731-35835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105731-42491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105523-91998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105523-41289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105524-58391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105524-95166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105524-15194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105524-61756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105523-41289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105358-99571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105358-23583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105358-16405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105358-95987.png)
(Ⅰ)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105359-93833.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105359-81543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105359-77002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105358-23583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105359-31973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105341-56766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105341-38965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105341-16216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105342-26375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105342-63486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105342-37056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105342-40353.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105302-57121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105302-73353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105302-46948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009105303-36624.png)
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