题目
题型:不详难度:来源:
在各项均为正数的等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-99860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-40535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-77645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-58124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-23199.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-99860.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-53111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-75958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-64129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-26700.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-76688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-18180.png)
解析
(1)因为项均为正数的等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-99860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-40535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101820-77645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-58124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101821-23199.png)
(2)由(Ⅰ)可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-76736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-58093.png)
解: (Ⅰ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-69861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-46082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-91975.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-63906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101824-24922.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101824-58204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101824-55933.png)
所以数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-69861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-76688.png)
(Ⅱ)由(Ⅰ)可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-76736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101823-58093.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101824-35695.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101825-95940.png)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101825-73542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101825-90843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101825-21711.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101822-18180.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101805-68029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101806-64968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101806-90958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101807-89899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101807-67255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101807-74651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101753-17207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-70956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-29328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-98792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-77710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-29328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101755-38213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101755-78084.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101753-17207.png)
(Ⅱ)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101755-49990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101754-77710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101755-98899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101755-66699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101756-63946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101756-41940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101744-33097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101744-67759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101745-31580.png)
A.![]() | B.6 | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101740-38162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101740-24395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101740-78123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101741-37294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101741-35250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101726-65385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101726-69209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012101726-90120.png)
A.120 | B.105 | C.90 | D.75 |
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