题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223930-40412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-81968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-18144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-11963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-94507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-58299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223932-63142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223932-50453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223932-33265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223932-91353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-90676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-65827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-89233.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223930-40412.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-46359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223934-87488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223934-38401.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223934-85244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223934-29041.png)
解析
试题分析:(1)首先设等差数列的公差为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-81968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-81968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-56645.png)
(2) 首先由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-90676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-95553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-84279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-18335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-46359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-43875.png)
“分离参数”得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-69198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-64931.png)
试题解析:(1)设等差数列的公差为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-81968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-43652.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-79043.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223937-66903.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223937-99864.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-56645.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223937-38971.png)
(2) 由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223933-90676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-95553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-84279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223937-50797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223938-40277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-18335.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223938-20939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223935-43875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223938-58942.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-64931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223931-11963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223938-42240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223936-64931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223939-15447.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223934-29041.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223912-58439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223912-26123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223912-41943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223912-62114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223913-91118.png)
A.512 | B.256 | C.81 | D.16 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223850-26983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223851-14244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223851-47340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223851-19914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223851-81322.png)
A.256 | B.81 | C.16 | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223841-39209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223841-69367.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223841-31941.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223841-70094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223800-62492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011223800-30004.png)
A.28 | B.33 | C.![]() | D.![]() |
A.an=8n-5(n∈N*) |
B.an=![]() |
C.an=8n+5(n≥2) |
D.an=8n+5(n≥1) |
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