题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-55771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-68693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-74855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-41726.png)
(1)证明:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-48767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-55771.png)
(2)在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002652-55771.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-16326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-65701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-87954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-83745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-66564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-30922.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-61766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-53585.png)
解析
试题分析:(1)证明一个数列为等比或等差数列,一般都是从定义入手,本小题首先需要将已知条件
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-52930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-11926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-38797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-21843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-48767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-60809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-54417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-11394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-69503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-95286.png)
(2)本小题首先假设在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-69495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-80803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-16451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-94457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-47490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-82339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-50229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-61766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-53585.png)
(3)本小题首先根据
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-16184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-57195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-81956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-54951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-63521.png)
试题解析:(1)将已知条件
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-52930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-11926.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-38797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-21843.png)
即数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-48767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-60809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002656-54417.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-29438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002701-20653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-11394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-69503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-95286.png)
(2)假设在数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-69495.png)
不妨设连续的三项依次为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002657-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-80803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-16451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-94457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002658-47490.png)
由题意得,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-82339.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002701-51476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002707-13184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002707-77217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002707-72398.png)
化简得,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002707-44983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-38983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-25984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-50229.png)
所以,存在满足条件的连续三项为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002654-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-61766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002655-53585.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-16184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-57195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-81956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-54951.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-87914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-63521.png)
由于若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-65701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
① 若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-99758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-91720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-40910.png)
② 若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-99199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002710-11152.png)
③ 若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-99758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-91720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-40910.png)
④ 若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-99758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-91720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002708-40910.png)
综上①②③④可知,只有当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002653-47482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002709-54782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-16184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002659-57195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002700-81956.png)
件点列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002710-61223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002710-94486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002710-70648.png)
核心考点
试题【已知数列中,,,.(1)证明:数列是等比数列,并求数列的通项公式;(2)在数列中,是否存在连续三项成等差数列?若存在,求出所有符合条件的项;若不存在,请说明理由】;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/20191012/20191012002631-63897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002631-93232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002632-16085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002632-48615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002632-87547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002632-16085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002632-48615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-84409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-37011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-97302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-23035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002540-90586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-23035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002540-76687.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002540-64529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-84409.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002540-57351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-37011.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002541-82317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-84409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002539-97302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002541-83996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002541-48570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002532-37020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002532-82606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002526-55478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002526-71443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002527-29339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002527-19449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002527-10986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002527-21391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002528-16263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002510-20719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002510-41175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002510-67404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002511-62042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002511-98804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012002511-44805.png)
最新试题
- 1有Xn-、Yn+、Z三种粒子,其核外电子层结构相同,则下列分析中不正确的是( )A.粒子半径大小的关系是Xn->Yn+
- 2(原创题)如图所示,将一根直径为4m的空心水泥圆柱,在其下方放入两根半径为0.5m圆木,当空心水泥圆柱与圆木相切于A,B
- 3《登州府志》记载,“纺织花布,以自衣被。穷乡山陬,无问男妇为之,其织作须织工。勤有余布,亦兼鬻于乡市,复有布贾贩之城市”
- 4下面是某同学整理的部分化学知识,其中有错误的是( )A.地壳中几种元素含量的比较:O>Si>AlB.构成物质的几种粒子
- 5下图机器的出现大大地促进了当时生产的发展,它的制造者是谁[ ]A、瓦特 B、卡尔·本茨 C、史蒂芬孙 D
- 6若某班从4名男生、2名女生中选出3人参加志愿者服务,则至少选出2名男生的概率为______.
- 7在探究滑动摩擦力的大小与哪些因素有关的实验中,小明同学认为滑动摩擦力的大小与物体运动的速度有关.请你利用下列器材设计一个
- 8(本小题满分10分)已知条件:和条件:,请选取适当的实数的值,分别利用所给的两个条件作为、构造命题“若则”,并使得构造的
- 9(12分)阅读材料,回答问题。材料下面是1960年我国中学历史教科书中“抗日战争”内容的目录摘编。第二十章全国抗日战争的
- 10下列每组物质中含有的化学键类型相同的是( )A.NaCl,HCl,H2O,NaOHB.Cl2,Na2S,HCl,S
热门考点
- 1不等式恒成立,则实数的取值范围是__________
- 2动点P在直线2x+y=0上运动,过P作圆(x-3)2+(y-4)2=4的切线,切点为Q,则|PQ|的最小值为______
- 3下列实验操作均要使用玻璃棒,其中玻璃棒作用相同的是① 过滤 ②蒸发 ③ 溶解 ④ 向容量瓶中转移液体A.①和④B
- 41787年宪法生效后,美国从一个松散的“邦联”发展成为一个统一的“联邦”。这一转变的重要意义有:①较好地协调了中央和地方
- 5“无为而治”是我国古老的政治智慧,在发展社会主义市场经济的今天,依然具有借鉴意义。浙江某市领导班子常用“无为而治”来概括
- 6已知集合,集合,又,则实数的取值范围是 ▲ .
- 7在如图所示的电路中,电池均相同,当电键S分别置于a、b两处时,导线MM′与NN′之间的安培力的大小分别为Fa、Fb,可判
- 8阅读下图,概括图表反映的信息。
- 9如图所示,小冬在实验室中用一个动滑轮匀速提升总重为2N的钩码,那么实际拉力F的大小可能是( )A.0.5NB.0.8N
- 10一个电子以与电场方向相同的初速度υ0,射入电场强度为E的匀强电场中,如图所示,已知电子电量e,电子质量m,试求:(1)