题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005313-52766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005313-20491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-44196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-97360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-17673.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-67202.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-85232.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-33090.png)
解析
试题分析:(1)根据题意可得当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-67202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-89148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-83081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-87235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-86027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-68040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-95592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-65821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-18886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-33090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-45808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-59189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-38385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-79459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-54618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-68706.png)
试题解析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005314-67202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-89148.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-83081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-87235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-86027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-68040.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-95592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005316-65821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-18886.png)
故此时满足条件的数列{an}共有3个:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005315-33090.png)
(2)令bi=
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-45808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-59189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005317-38385.png)
反之,由符合上述条件的7项数列{bn}可唯一确定一个符合条件的8项数列{an}. 7分
记符合条件的数列{bn}的个数为N.
显然,bi (1≤i≤7)中有k个2;从而有k个
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-79459.png)
当k给定时,{bn}的取法有
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-54618.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005318-68706.png)
因此,符合条件的数列{an}的个数为393. 10分
核心考点
试题【设数列{an}共有n()项,且,对每个i (1≤i≤,iN),均有.(1)当时,写出满足条件的所有数列{an}(不必写出过程);(2)当时,求满足条件的数列{a】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005306-79422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005307-43631.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005258-28123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005258-69974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005258-97085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005258-88173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005258-39909.png)
A.![]() | B.![]() | C.![]() | D.![]() |
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-52886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-12786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-18433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-46919.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-52886.png)
(2)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-52886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005141-33759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005142-77028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005120-23594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005120-83937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005120-86630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005121-54670.png)
(1)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005120-23594.png)
(2)是否存在正整数n和k,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009005121-52927.png)
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