题目
题型:不详难度:来源:
若等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-25578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-47126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-26162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-72824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
(1)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-50317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
(2)若首项为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-48024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-25578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
(3)若首项为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-48024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-25578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-29958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-45312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-64316.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-56706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-25786.png)
(3)最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-14127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-22512.png)
解析
试题分析:(1)由等差数列的通项公式找出等差数列的首项和公差,然后利用等差数列的前n项和的公式表示出Sn和S2n,求出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-72824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-31464.png)
(2)设此数列的公差为d,根据首项和公差,利用等差数列的前n项和的公式表示出Sn和S2n,因为此数列为S数列,得到
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-72824.png)
(3)根据已知条件首项为a1的各项为正数的等差数列{an}为S数列,设n+h=2008,利用基本不等式求出
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-12735.png)
解:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-50317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-74212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080636-16430.png)
(2)假设存在等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-25578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080639-56193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080639-76741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080639-17192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080639-55621.png)
由于①对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080635-47126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080640-50980.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080640-91320.png)
其通项公式为:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-56706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080637-25786.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080640-84208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080640-49562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080641-24676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080641-96482.png)
其最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-14127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080638-22512.png)
点评:解决该试题的关键是学生灵活运用等差数列的通项公式及前n项和的公式化简求值,掌握题中的新定义并会利用新定义化简求值。
核心考点
试题【(本题满分14分)若等差数列的前项和为,且满足为常数,则称该数列为数列.(1)判断是否为数列?并说明理由;(2)若首项为且公差不为零的等差数列为数列,试求出该数】;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/20191012/20191012080628-15858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080629-52510.png)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080617-87731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080618-34936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080618-87556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080618-85116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080618-52210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080618-76650.png)
等差数列{an}不是常数列,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080550-65502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080550-22209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080550-41959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080551-89065.png)
(1)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080551-23642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080550-41959.png)
(1)已知正项等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080534-84425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080534-18575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080535-25026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080535-67767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080535-17736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080534-84425.png)
(2)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080535-45876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080535-57857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080536-53487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080536-96263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080524-94520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080524-14834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080525-71202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080525-62582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080525-20108.png)
(Ⅰ)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080525-32188.png)
(Ⅱ)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080526-11754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080526-30439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012080526-52585.png)
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