题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-27342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-22649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-82000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-23926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-65112.png)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-49635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-27342.png)
(II)在(I)的条件下,若等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-21294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-22649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-43800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-63243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-68937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-90678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-14692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-47932.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-22688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-86851.png)
解析
(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-13567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-66713.png)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-66702.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-21294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-63243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-99016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-62030.png)
故可设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-92316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-34614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-78171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084028-59868.png)
解:(I)由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-13567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-66713.png)
两式相减得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084026-66702.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084028-30084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-27342.png)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084028-35836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-27342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084028-42300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-22688.png)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-21294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-63243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-99016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-62030.png)
故可设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-92316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-34614.png)
由题意可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084027-78171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084028-33395.png)
∵等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084024-21294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084023-22649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084025-47932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084029-90311.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084029-40192.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084011-74290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084011-86593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084011-69912.png)
A.5 | B.6 | C.8 | D.10 |
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084006-21635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084006-27807.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084006-21635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084006-29502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084006-33708.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083959-78015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083959-47842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083959-78015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083953-38540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083953-23964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083954-81608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083954-45068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083954-18553.png)
A.55 | B.95 | C.100 | D.不能确定 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083942-85633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083942-84523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083942-88510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083943-10136.png)
(1)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083942-88510.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083942-85633.png)
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