题目
题型:陕西省模拟题难度:来源:
(Ⅰ)求此四数;
(Ⅱ)若前三数为等差数列{an}的前三项,后三数为等比数列{bn}的前三项,令
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092835-17186.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092835-83175.png)
由题意知a=4,d=2
所求四数为2,4,6,9
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092836-82130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092836-58847.png)
核心考点
试题【已知四个正实数前三个数成等差数列,后三个数成等比数列,第一个与第三个的和为8,第二个与第四个的积为36. (Ⅰ)求此四数; (Ⅱ)若前三数为等差数列{an】;主要考察你对数列综合等知识点的理解。[详细]
举一反三
( 1) 求此四数;
(2)若前三数为等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092830-48727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092830-25560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092830-35872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092831-91767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092831-36200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092827-17704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092827-23469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092827-56323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092827-57509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092827-17974.png)
已知数列{an}的前n项和为Sn,满足.
(Ⅰ)求数列{an}的通项公式an;
(Ⅱ)令,且数列{bn}的前n项和为Tn满足
,求n的最小值;
(Ⅲ)若正整数m,r,k成等差数列,且,试探究:am,ar,ak能否成等比数列?证明你的结论.
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092757-82947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092757-59922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092758-16182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092758-40331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092758-25868.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092758-64975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092759-91143.png)
(Ⅱ)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092759-37987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092759-97310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092759-46963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092759-19448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092800-19434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092800-81318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092746-36961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092746-70770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092746-75970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092746-21339.png)
(1)证明:对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092747-84959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092747-94714.png)
(2)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092747-87787.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092747-74377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015092748-91957.png)
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