题目
题型:不详难度:来源:
(本小题满分12分)
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225407-62601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225408-95210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225408-95540.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-53970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-41255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-67779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-47067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-12117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-52400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-89873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-11106.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225407-62601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-41255.gif)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-17215.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-76355.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-86551.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-40328.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225408-95540.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-53970.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-39030.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225412-55390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225412-92911.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225412-81773.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225412-69820.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225413-35450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225413-96263.gif)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225407-62601.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-76355.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225413-70386.gif)
在等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-41255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-12117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225413-26898.gif)
又因
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-52400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-89873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225410-11106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-41255.gif)
∴(
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225413-19058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225414-15221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225414-96058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225414-21092.gif)
解得d=-10,或d="2," ∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-67779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225409-47067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225414-53077.gif)
∴bn=2n+1
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-86551.gif)
(Ⅱ)由(Ⅰ)知
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225415-69803.gif)
=(
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225415-97250.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225415-15678.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225411-40328.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225355-96692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225357-39211.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225357-38555.gif)
(Ⅱ)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225355-96692.gif)
前后两项之和,则这个数列的
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225340-91215.gif)
已知△ABC中,角A、B、C成等差数列,求证:+=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225334-47506.gif)
已知:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225323-68253.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225323-49782.gif)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225323-55555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-70926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-38091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-26326.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-70926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-48265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225315-50666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225316-16434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012225316-61015.gif)
A. 4 | B. 3![]() | C. 2 | D. 1 |
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