真题
1 . 无穷等比数列
满足首项
,记
,若对任意正整数
集合
是闭区间,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b67857a043caf87b55d38401d0d9062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d59e4e49e9b0b2493f18b41e260da5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72f2cbabcb955a433e99bf0ee8ec020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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解题方法
2 . 已知无穷数列
的前
项和为
,不等式
对任意不等于2的正整数
恒成立,且
,那么这样的数列有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d896cc62945587c910c3ea157d1bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80759fdc78c76b05dab66c325f48a443.png)
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3 . 设关于x的方程
的从小到大的第i个非负解为
,若数列
是无穷等差数列,且
在区间
中的项恰好比在区间
中的项少2项,则ω的取值集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4aef8fc10674359b41c70424c7b696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45016247370f5b00aeb0882977abb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583dfca240679328ffcbbe457ec5bdd8.png)
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4 . 设无穷正数数列
,如果对任意的正整数
,都存在唯一的正整数
,使得
,那么称
为内和数列,并令
,称
为
的伴随数列,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a03aa8aecce705d71b3b6d906443b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d30acf705ccad76fb8679f796663c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若内和数列![]() ![]() |
D.若内和数列![]() ![]() ![]() |
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2024-06-01更新
|
621次组卷
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2卷引用:上海市 位育中学2023-2024学年高三下学期三模数学试题
5 . 设
为数列
的前
项和,有以下两个命题:①若
是公差不为零的等差数列且
,
,则
是
的必要非充分条件;②若
是等比数列且
,
,则
的充要条件是
.那么( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615d2684f4ecc3f628bedc65da339931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750a0eaa543fd3dfc8e3859ecf774344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0163fabbac9f7824835d3d96d7b70cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8e90d52301bbdbe6162603db405020.png)
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是真命题 | D.①、②都是假命题 |
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解题方法
6 . 已知数列
是给定的等差数列,其前
项和为
,若
,且当
与
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d065b001d48a52d4a9e28182cf9373f.png)
取得最大值,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07948544351dd327cb43c8d36280653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235c5ec0f01ce8c3af2191116cab3e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca4f2b82d9d7a8323c8d697338a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d065b001d48a52d4a9e28182cf9373f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a3d0379a536cb2ec9d6647e165bf48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49a8861a57e5de89b2bd94ab55c9163.png)
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2024-04-24更新
|
318次组卷
|
2卷引用:上海市黄浦区2024届高三二模数学试题
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解题方法
7 . 已知平面向量
、
、
满足:
,
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f6c22b8e3959e74f3226fb2e0e2c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e840b7ca6ef881f931cc5abc1b1ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c187a1fe19511b52d7f1d2ddf9d673c.png)
您最近一年使用:0次
2024-04-23更新
|
539次组卷
|
2卷引用:上海市金山区2024届高三二模数学试题
8 . 设数列
的前
项和为
,若存在非零常数
,使得对任意正整数
,都有
,则称数列
具有性质
:①存在等差数列
具有性质
;②不存在等比数列
具有性质
;对于以上两个命题,下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfdfb64f33ff54ec06e98975c17b2034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.①真②真 | B.①真②假 | C.①假②真 | D.①假②假 |
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解题方法
9 . 已知平面上有
个点
,
,
,
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bdda8ec472fb7f07c7213bf6f063b1.png)
且
,记
的坐标为
,将
,
,
依次顺时针排列,求
=________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f18f1cec532d6835b69b99704df0d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688d97dccaf3c1259e2f1f8fd525bedc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bdda8ec472fb7f07c7213bf6f063b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd43fd553146f09a4381dcdbf0458cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceec3ca529adb8c49f9e3db40256e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2b289b20ecde54bf91c3a0bd5869e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c97d15ede1ffecd6035c4e196e557f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85462bd19666677a46625c60deadd979.png)
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2023-12-16更新
|
297次组卷
|
4卷引用:上海市嘉定区2024届高三上学期质量调研数学试题
上海市嘉定区2024届高三上学期质量调研数学试题上海市普陀区长征中学2024届高三上学期10月月考数学试题(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第16题 数列递推求通项(高三二轮每日一题)
名校
解题方法
10 . 蜀绣又名“川绣”,与苏绣,湘绣,粤绣齐名,为中国四大名绣之一,蜀绣以其明丽清秀的色彩和精湛细腻的针法形成了自身的独特的韵味,丰富程度居四大名绣之首.1915年,蜀绣在国际巴拿马赛中荣获巴拿马国际金奖,在绣品中有一类具有特殊比例的手巾呈如图所示的三角形状,点D为边BC上靠近B点的三等分点,
,
.
,求三角形手巾的面积;
(2)当
取最小值时,请帮设计师计算BD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bdcd23d2c26d9df0b4756d8a715673.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
您最近一年使用:0次
2023-07-12更新
|
1849次组卷
|
9卷引用:上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题
上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题四川省成都市府新区2022-2023学年高一下学期期末数学试题江苏省镇江市丹阳高级中学2024届高三下学期2月阶段检测数学试题重庆市万州区万州第一中学2023-2024学年高一下学期3月月考数学试题广东省深圳市龙华区深圳市致理中学2023-2024学年高一下学期3月月考数学试题重庆市乌江新高考协作体2023-2024学年高一下学期第一阶段学业质量联合调研抽测(4月)数学试题福建省泉州市泉州一中、泉港一中、厦外石狮分校三校联盟2023-2024学年高一下学期5月期中联考数学试题河南省信阳市信阳高级中学贤岭校区2023-2024学年高一下学期6月月考数学试题四川省南充高级中学2023-2024学年高一下学期第二次月考(5月)数学试卷