题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215939-99801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215939-37596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-91057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-97466.png)
(1) 求常数
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-49964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215939-99801.png)
(2) 若抽去数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215939-99801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-79996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-79280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-79280.png)
(3) 在(2)的条件下,设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-79280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-14176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-87083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-14176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-85977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-14176.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-49964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-69859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215942-99915.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215942-75336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215942-72196.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215942-79518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215943-79172.png)
又因为存在常数p使得数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215943-31588.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215943-92551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215943-29853.png)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215943-31588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-69859.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215944-24175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215940-49964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215941-69859.png)
第二问中,解:由等比数列的性质得:
(i)当
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215944-22302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215944-63982.png)
(ii) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215944-95689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215945-17998.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215942-99915.png)
第三问假设存在正整数n满足条件,则
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215945-31340.png)
则(i)当
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215944-22302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215945-37237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215945-30160.png)
核心考点
试题【已知数列是首项为的等比数列,且满足.(1) 求常数的值和数列的通项公式;(2) 若抽去数列中的第一项、第四项、第七项、……、第项、……,余下的项按原来的顺序】;主要考察你对数列的概念与表示方法等知识点的理解。[详细]
举一反三
①
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215911-79882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215911-51821.png)
(1)若{an}是等差数列,Sn是其前n项的和,a3=4,S3=18,试探究{Sn}与集合W之间的关系;
(2)设数列{bn}的通项为bn=5n-2n,且{bn}∈W,M的最小值为m,求m的值;
(3)在(2)的条件下,设
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215911-43209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215814-82778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215815-90021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215815-70898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215815-39407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215815-95128.png)
A.一定是等比数列 |
B.一定不是等比数列 |
C.有可能是等比数列,也有可能不是等比数列 |
D.一定不是等差数列 |
在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-25507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-41057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-57901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-57842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215724-50289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-25507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-57842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215724-34979.png)
(1)证明:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215724-68239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215723-25507.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215724-34979.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215724-71526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215725-56553.png)
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215641-51091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-34116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-68115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-80828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-76910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-34116.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215641-51091.png)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215643-54698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215643-35730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215642-34116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215643-95899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215643-31019.png)
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215500-96041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215501-77817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215501-11997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215501-30586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215502-26208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215502-80284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215502-88924.png)
(Ⅰ)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215503-76022.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215503-11927.png)
(Ⅲ)是否存在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215503-70725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215503-81839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191007/20191007215503-70725.png)
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