题目
题型:不详难度:来源:
若等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-81731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-64857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-46163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-15917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
(1)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-99103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
(2)若首项为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-18689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-81731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
(3)若首项为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-18689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-81731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051534-73613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051534-51679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051534-44452.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051534-72745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-27190.png)
(3)最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-90534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-46379.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/20191010/20191010051532-15917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-98004.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/20191010/20191010051532-15917.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/20191010/20191010051536-51433.png)
解:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-99103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051536-78191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051533-17775.png)
(2)假设存在等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-81731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051536-21957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051536-85456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051542-86107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051543-66307.png)
由于①对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051532-64857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051543-32836.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051543-96978.png)
其通项公式为:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051534-72745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-27190.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051543-16069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051543-20689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051544-75876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051544-32532.png)
其最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-90534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051535-46379.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/20191010/20191010051435-89291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051435-93722.png)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051414-90441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051414-27227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051414-97519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051415-60956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051415-47684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051415-99397.png)
等差数列{an}不是常数列,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051402-60816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051403-80251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051403-23185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051403-93630.png)
(1)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051403-62546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051403-23185.png)
(1)已知正项等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051156-17394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051156-80550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051156-91521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051157-37724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051157-72349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051156-17394.png)
(2)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051157-93962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051157-42907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051158-83978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051158-16874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051113-50133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051113-69542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051114-29707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051114-65808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051114-49279.png)
(Ⅰ)求数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051114-83677.png)
(Ⅱ)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051115-13623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051115-31454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010051115-33573.png)
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