题目
题型:不详难度:来源:
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224504-17802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224504-28015.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224505-46460.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224505-59658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224505-32634.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224506-90105.gif)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224504-17802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224505-59658.gif)
(2) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224506-96413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224506-74540.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224506-96413.gif)
答案
所以an=4n-1.…………………………………………………………………………4分
设{ bn }的公差为d,由5S5=2 S8得5(5 b1+10d)=2(8 b1+28d),
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224506-40398.gif)
所以bn=b1+(n-1)d=3n-1.…………………………………………………8分
(2) Tn=1·2+4·5+42·8+…+4n-1
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224507-11765.gif)
4Tn=4·2+42·5+43·8+…+4n(3n-1),②
②-①得:3Tn=-2-3(4+42+…+4n)+4n(3n-1)……………………………10分
= -2+4(1-4n-1)+4n(3n-1)
=2+(3n-2)·4n………………………………………………………12分
∴Tn=(n-
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224507-77674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224507-77674.gif)
解析
核心考点
举一反三
已知{an}是递增的等差数列,满足a2·a4=3,a1+a5="4."
(1) 求数列{an}的通项公式和前n项和公式;
(2) 设数列{bn}对n∈N*均有
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224459-45928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224459-24564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-28295.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-49701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-74562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-87791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-45792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-24531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-24531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-43704.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-78524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-90850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-85283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-66622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224435-99036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-94008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-53760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-21092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224434-81711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-64627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-96083.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224437-25726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224437-99511.gif)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224437-31038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224437-94313.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224437-21040.gif)
(2) 设曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224433-39443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224436-94008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224438-21923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224438-91703.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224438-91703.gif)
(3) 在满足(2)的条件下, 若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224438-74434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224438-36705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224439-27136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224439-65648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224439-76017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224439-56579.gif)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224426-68465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224426-47603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224426-27978.png)
A.1033 | B.1034 | C.2057 | D.2058 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224420-99420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224421-48846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224421-33287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224421-38336.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224404-16911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224404-33261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224405-12306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224405-83417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012224404-33261.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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