题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035148-18034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-10503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-25459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035148-18034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-85149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-49379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-85149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035148-18034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-39515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-56982.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-24128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-75885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-66378.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035151-47885.png)
解析
试题分析:本题第(1)问,直接根据条件
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035149-10503.png)
第(2)问,先假设其存在,然后根据等差数列对应的相邻两项的差为常数即可求出λ的值;
第(3)问,先根据条件求出数列{an}的通项公式,再借助于分组求和以及错位相减求和即可求出结论.
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-24128.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035151-54260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035151-40074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035151-61804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035152-42161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-75885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035150-66378.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035152-95287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035152-13572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035152-51310.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035152-36832.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035153-57668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035153-17248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035153-66418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035153-58334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035154-27800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035151-47885.png)
点评:本题主要考察利用数列的递推式求数列的特定项以及数列的求和问题.本题涉及到数列求和的分组法以及错位相减法,错位相减法适用于一等差数列与一等比数列相乘组成的新数列.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035136-84182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035137-59082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035137-94891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035137-17862.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035137-59082.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035137-54593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035138-69016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035138-25024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035124-41021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-63559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-41591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-70247.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035124-41021.png)
(2)在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035124-41021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-28778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-19207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-63559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035126-47118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035126-58202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035126-21580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035125-63559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035126-17956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035114-34744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035114-86666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035114-86666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035114-29811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035114-98483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035115-70162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035115-36196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035115-80834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035115-41849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035116-97316.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035058-26003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035058-10061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035059-67884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035059-95643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035059-51949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035059-70777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035059-24812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035100-53253.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035100-63578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035100-45520.png)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035100-76787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035050-62643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035051-68245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035051-96690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035051-85682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035051-52020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035051-95772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-30946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-59006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-30873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-97022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-26535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035052-79840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035053-38738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191015/20191015035053-11807.png)
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