题目
题型:不详难度:来源:
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-19213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-31120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-18860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-93919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-63039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-52518.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-19213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010050-93919.png)
(2) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-33801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-20156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-33801.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-53590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-53590.png)
解析
试题分析:(1) 设{an}的公比为q,由a5=a1q4得q=4
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/20191010/20191010010052-14863.png)
所以bn=b1+(n-1)d=3n-1. 8分
(2) Tn=1·2+4·5+42·8+ +4n-1(3n-1),①
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/20191010/20191010010051-53590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-53590.png)
点评:中档题,本解答从研究
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010052-19904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-33801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010051-20156.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010037-92229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010037-93841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010037-73559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010038-52708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010010037-92229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005756-82253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005757-98940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005757-53141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005757-42837.png)
A.14 | B.15 | C.16 | D.75 |
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-82825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-58005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-75513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005721-65633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005721-72684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005721-15331.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005721-34251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
(Ⅱ)试写出a30关于
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
(Ⅲ)续写已知数列,可以使得
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005722-78590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005722-18468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005722-67810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005722-29405.png)
(Ⅳ)在(Ⅲ)条件下,且
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005723-98457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005720-92378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005723-56275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005640-26228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005640-82032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005640-15138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005640-60428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005641-41744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005527-82901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005527-51535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005528-77751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005528-72394.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005528-71959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005528-59729.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005529-38188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005529-53002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010005529-28037.png)
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