题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-69046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-25528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-95694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-64905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-26342.png)
且满足:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-40426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-97531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-25528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-53454.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-26342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-64905.png)
(Ⅲ)是否存在正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-16173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-19789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-12351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-16173.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-21236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-23316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-10839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-75119.png)
解析
(Ⅰ)根据Sn求出a1,a2,a3,根据{an}为等比数列,确定出c的值.
(Ⅱ)根据bn+1=
bn |
1+2bn |
(Ⅲ)先求出Tn,假设满足T1,Tm,Tn成等比数列,得到n与m的关系式,再根据1<m<n,求出m,n的范围,根据m,n是正整数,求出m,n的值.
解:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-41820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-27832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091605-47852.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-69046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091605-81196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091603-21236.png)
经检验此时
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091601-69046.png)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091602-40426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091605-54831.png)
数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091606-50218.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091606-82773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091606-84559.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-23316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-10839.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091606-37646.png)
假设存在正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091606-15665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091607-94908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091607-32395.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091607-46232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091608-59513.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091608-26293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091608-24395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091608-28559.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091608-41822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091609-20090.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091609-83465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091609-58165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091609-50516.png)
所以满足题意的正整数存在,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091604-75119.png)
核心考点
试题【已知等比数列的前项和为,正数数列的首项为,且满足:.记数列前项和为.(Ⅰ)求的值; (Ⅱ)求数列的通项公式;(Ⅲ)是否存在正整数,且,使得成等比数列?若存在,求】;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/20191012/20191012091556-45767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091556-10201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091556-33449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091557-36022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091557-10643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091557-50905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091557-34852.png)
A.8 | B.7 | C.6 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-95984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-88908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-95984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-80844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-30869.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-95984.png)
(2)对
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-39002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091543-66905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091544-98375.png)
A.90 | B.45 | C.30 | D.![]() |
(1)求数列{an}的通项公式;
(2)数列{bn}满足bn=(-3)n·an,求数列{bn}的前n项和Tn.
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091444-82467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091444-42144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091444-82467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091444-92131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012091444-83690.png)
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