题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-37315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-74362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-37315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-11373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-74362.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-46362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-33249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-66461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-46362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-62606.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-95837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173153-49451.png)
解析
试题分析:(1)已知等差数列的首项和公差,可直接利有公式
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173153-99816.png)
(2)利用(1)的结果求出
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173153-38509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-66461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-46362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-33249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173153-79908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-46362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-62606.png)
解:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-37315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173153-31686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173154-95608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173154-30655.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173154-48732.png)
(2)由(1)得,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173154-34256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173152-66461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173154-31762.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-74343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-64441.png)
又因
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-11503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-73475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-64441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173156-97232.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173155-73475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173156-39606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011173151-75315.png)
核心考点
举一反三
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172912-77026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172912-85561.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172912-38512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172913-51460.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172912-77026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172913-48332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172913-42392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172913-71230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172913-48332.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172914-47335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172914-90397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172914-28516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172914-28516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172914-47335.png)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-81268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-65248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-47281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-31710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-13899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-71252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-81268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-25720.png)
(1)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-81268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-65248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-48805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-81268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-25720.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-55265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-12817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-46254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172821-81268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-25720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-10228.png)
(3)证明:对任意的等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172823-55265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172822-25720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172824-63936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172824-47090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172824-57693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172824-25915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172707-27380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-17805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-11454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-16740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-87519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-87181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-87519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172708-11454.png)
在等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172644-18053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172644-94205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172645-44614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172645-86646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172645-63296.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172644-18053.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172645-24077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172646-79742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172646-94601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-55524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-36831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-76151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-12569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-69258.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-12569.png)
(1)求证数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-73163.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-73341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-83569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-93066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172327-12569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172328-93066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011172329-89651.png)
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