题目
题型:不详难度:来源:
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083211-77027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083211-49446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083211-73276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-17557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-38471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-82679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-15816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-18397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-53314.png)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083211-77027.png)
(2) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-45538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-65067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-37521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083214-84892.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083214-76213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083214-60236.png)
解析
(Ⅰ)设等差数列{an}的公差为d,d>0,利用等差数列的通项表示已知,求解出d,a1,结合等差数列的通项即可求解
(Ⅱ)数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-17557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-38471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-82679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083212-15816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-18397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-53314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083215-31433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-45538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083215-36952.png)
解: (1) 解: 设等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083215-73670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-41813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-66619.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-26600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-76379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-86629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083221-35844.png)
(2) 由(1)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083222-46125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083222-40394.png)
b1=1,当n≥2时,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083222-92846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083222-74760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083228-85713.png)
因而
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083215-31433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083222-40394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083213-45538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083215-36952.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083214-84892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083229-64314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083229-54198.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083229-62740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083229-13761.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083229-27475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083230-70298.png)
①-②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083230-42233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083230-10154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083230-76115.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083231-50630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083214-60236.png)
核心考点
试题【(本题满分12分)已知是一个公差大于的等差数列,且满足.数列,,,…,是首项为,公比为的等比数列.(1) 求数列的通项公式;(2) 若,求数列的前项和.】;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/20191012/20191012083156-44717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-66240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-83690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-45341.png)
恒有
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-99148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-58213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083157-23650.png)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-44717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083156-66240.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083157-90143.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083157-40270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083157-93756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083157-35387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083158-30613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083158-19699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083203-70544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083144-87235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083150-81477.png)
A.![]() | B.![]() | C. 31 | D. 64 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083134-28193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083134-90149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083134-98299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083135-43822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083135-52099.png)
A.若 ![]() ![]() |
B.若数列 ![]() ![]() |
C.若数列 ![]() ![]() ![]() |
D.若对于任意的![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083115-34021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083115-76047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083115-76645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083115-80904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083115-12078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083116-41800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083116-99507.png)
A.18 | B.19 | C.29 | D.30 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083105-94589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083105-47865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083106-98638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083106-96909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083106-89379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083106-61993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083107-51815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083107-94604.png)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083107-18702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083107-84692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083107-85485.png)
(II) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083108-27399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083108-55547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083108-71431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083109-40519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012083105-47865.png)
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