名校
1 . 已知
为数列
的前
项和,
,
,平面内三个不共线的向量
,
,
满足
,若点
,
,
在同一直线上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b30c3d7cc1e41af67e909df3f39830.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911c0a2ab5e2e85f1ad267f41cb96b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794efd8cf0cc386faa170d01f357b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7195a0b5b59c9462b9faaf5a9fcfc6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b855acafb6c888420224f6f052f416c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b30c3d7cc1e41af67e909df3f39830.png)
您最近一年使用:0次
2019-11-14更新
|
408次组卷
|
2卷引用:上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题
2 . 设数列
是首项为0的递增数列,函数
满足:对于任意的实数
,
总有两个不同的根,则
的通项公式是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7535ab1819efecd58e89dbf65e1aa0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c91d6d2c9deb4722c6a7b21358b213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa2524fcaedaeb1a8b55df6d8c9bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次
2019-11-13更新
|
1235次组卷
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20卷引用:2017届河南郑州一中网校高三入学测试数学(理)试卷
2017届河南郑州一中网校高三入学测试数学(理)试卷2016-2017学年湖北宜昌葛洲坝中学高二理上期中数学试卷12016-2017学年湖北宜昌葛洲坝中学高二理上期中数学试卷2河北省武邑中学2017届高三下学期一模考试数学(文)试题【全国百强校】福建省厦门外国语学校2019届高三11月月考数学(理)试题上海市金山中学2016-2017学年高一下学期期末数学试题上海市南洋模范中学2018-2019学年高三上学期第一次月考数学试题2018届上海市大同中学高三上学期期中数学试题上海市七校(北虹,上理工附中,同二,光明,六十,卢高,东昌)2016届高三下学期3月联考(理)数学试题2016届上海市七校联考高考一模(理科)数学试题上海市理工附中等七校2016届高三下学期3月联考(文)数学试题上海市七校2016届高三下学期3月联考(文)数学试题福建省泰宁第一中学2020届高三上学期第二次阶段考试数学(理)试题(已下线)第7章 三角函数(能力提升)-2020-2021学年高一数学下册单元测试定心卷(沪教版2020必修第二册)(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)上海期末真题精选50题(小题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)专题4-1 三角函数性质、最值和w小题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)上海市建平中学2021届高三冲刺模拟卷3数学试题(已下线)专题06 三角函数(模拟练)-1上海市西南位育中学2021-2022学年高二下学期期末数学试题
名校
3 . 数列
的通项公式
,其前
项和为
,则
等于_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06dd07bcdcf34c4cbeb9a07462407e2.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/453e398c6f4b0f5247906161e084ed2d.png)
您最近一年使用:0次
2019-07-01更新
|
799次组卷
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2卷引用:浙江省金华市曙光学校2019-2020学年高一下学期返校测试数学试题
名校
4 . 对于数列
,定义
为
的“优值”,现已知某数列的“优值”
,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1226620ac12f4e28ee5461c95a83538c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4caa2574d37de2def69f51e81b0f553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466a22f3320bb2340bab262cab2d713e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/1226620ac12f4e28ee5461c95a83538c.png)
A.2022 | B.1011 | C.2020 | D.1010 |
您最近一年使用:0次
2018-12-17更新
|
2548次组卷
|
8卷引用:黑龙江省哈尔滨师范大学青冈实验中学校2019-2020学年高二上学期开学考试(8月)数学试题
黑龙江省哈尔滨师范大学青冈实验中学校2019-2020学年高二上学期开学考试(8月)数学试题湖南省岳阳市汨罗市二中2020-2021学年高三上学期入学考试数学试题【全国百强校】湖南师范大学附属中学2019届高三上学期月考(四)数学(理)试题湖南省邵东县创新实验学校2019届高三第五次月考数学(理)试题2020届湖南省长沙市长郡中学高三上学期月考(四)数学(文)试题2019届湖南师大附中高三月考试卷(四)数学(理科)试题四川省宜宾市叙州区第二中学2020-2021学年高三上学期阶段二考试数学(文)试题(已下线)第4章 数列(基础卷)-2021-2022学年高二数学新教材单元双测卷(苏教版2019选择性必修第一册)
名校
5 . 已知数列
的前
项和
满足
,且
,数列
满足
,
,其前9项和为36.
(1)求数列
和
的通项公式;
(2)当
为奇数时,将
放在
的前面一项的位置上;当
为偶数时,将
放在
前面一项的位置上,可以得到一个新的数列:
,求该数列的前
项和
;
(3)设
,对于任意给定的正整数
,是否存在正整数
,使得
成等差数列?若存在,求出
(用
表示);若不存在,请说明理由.
![](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/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3d3ec1d130b7d6ca21410c9dc71965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a1296484150c082ac7ec72e82a8be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37bd079cf3329af20b2609b08c9f8c4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da36c3e94453b76b85568daf9411e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b52c4c6c26644547d8e3542510529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505b3b01eabf49fa1cd907fe92deb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f6addd1b216f3bb7d7e0f0ccd3aff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd8a8d7d8b468a3ab46ecb356ce1ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccc19a183b9ce7f82d2609a14b9a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-05-16更新
|
392次组卷
|
2卷引用:上海交通大学附属中学2020届高三下学期开学考试数学试题
名校
6 . 设数列
满足:①
;②所有项
;③
.
设集合
,将集合
中的元素的最大值记为
.换句话说,
是
数列
中满足不等式
的所有项的项数的最大值.我们称数列
为数列
的
伴随数列.例如,数列1,3,5的伴随数列为1,1,2,2,3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33625a68f7913210ce0b69cbbbc1f8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a418f13ac663b2b0458f99763fee8581.png)
设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ee631c704aa48b5ff22d0fe0507eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19db2869aeaf97debfa2e2f9a4843a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
伴随数列.例如,数列1,3,5的伴随数列为1,1,2,2,3.
(1)若数列的伴随数列为1,1,1,2,2,2,3,请写出数列
;
(2)设,求数列
的伴随数列
的前100之和;
(3)若数列的前
项和
(其中
常数),试求数列
的伴随数列
前
项和
.
您最近一年使用:0次
2018-01-18更新
|
404次组卷
|
3卷引用:上海市南洋模范中学2017-2018学年高三下学期开学考试数学试题
7 . 若
或
,则称
为
和
的一个
位排列,对于
,将排列
记为
,将排列
记为
,依此类推,直至
,对于排列
和
,它们对应位置数字相同的个数减去对应位置数字不同的数,叫做
和
的相关值,记作
,例如
,则
,
,若
,则称
为最佳排列.
(Ⅰ)写出所有的最佳排列
.
(Ⅱ)证明:不存在最佳排列
.
(Ⅲ)若某个
(
是正整数)为最佳排列,求排列
中
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aa0f4cff7395ae1943c6624bedff15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484227f07b23879a11207e1ce0c2a51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69be4f6649db586cb61f27177a8e31b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9730694838cb4eac8aeac5613f722b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375e799388a7380501b14e2b2a469e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df487f36154ed93c8752b919ab500675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418eb157282e922d3acf5488dcc5b49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b80f28c33bb84e04861f08f064a0ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27676ab31f7b7fee04e6719275d7febf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae55b1aad1585aa5732d468f83a0483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0746ade04116b44bc675d6bdb2075d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfdcf0a95b4c1a2ad293fdec932994f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f97a1ee8a5a1bb710de04c38a3c79fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519482116da1a328a9c16525c09ba4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(Ⅰ)写出所有的最佳排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(Ⅱ)证明:不存在最佳排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(Ⅲ)若某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d074c8ac48227c468fc562a34bfd93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d074c8ac48227c468fc562a34bfd93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
2018-01-13更新
|
499次组卷
|
2卷引用:北京东城区171中学2018届高三上学期期中考试数学试题
8 . 已知数列
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
是等比数列
(II)求数列
的通项公式
(III)设
,若
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631307e8ff61b215f447f2527c36e04.png)
(II)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(III)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9dfeeff5b7c543226a16dac4509375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23487d83aa14650649f1e0b636acabb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6143b63cb006d60ffb578a90da8f9f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-12-11更新
|
3797次组卷
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11卷引用:湖北省黄冈市黄梅国际育才高级中学2019-2020学年高一下学期复学考试数学试题
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名校
解题方法
9 . 等差数列
中,已知
,且
,
,
为递增的等比数列.
(1)求数列
的通项公式;
(2)若数列
的通项公式
(
),求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1e1f0eaefb104198c420d34a581e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2017-05-16更新
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644次组卷
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2卷引用:河南省郑州市第一中学2018届高三上学期入学考试数学(理)试题
名校
10 . 已知数列
满足
,
,
,记
,
分别是数列
,
的前
项和,证明:当
时,(1)
;(2)
;(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab335212fe8d8b99d3cf35c5db14c36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7118a8dab6f8e5346ebc3788cea66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1254070260067f8bf2fec39a7d0c8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461213d375554bfe8641284dc283383f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c3b913993e1ae3ecca430abc73b43c.png)
您最近一年使用:0次
2017-02-08更新
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1443次组卷
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3卷引用:安徽省合肥市四校2019-2020学年高二上学期开学考试数学试题