名校
解题方法
1 . 已知等比数列
的公比为q(
),其所有项构成集合A,等差数列
的公差为d(
),其所有项构成集合B.令
,集合C中的所有元素按从小到大排列构成首项为1的数列
.
(1)若集合
,写出一组符合题意的数列
和
;
(2)若
,数列
为无穷数列,
,且数列
的前5项成公比为p的等比数列.当
时,求p的值;
(3)若数列
是首项为1的无穷数列,求证:“存在无穷数列
,使
”的充要条件是“d是正有理数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45482d31d1d7448c9f3922b4d2a55331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8f1df735a4480e538fd1d067fbd577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c0d25496e9b663eeb6bf77245d326e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980995738642db660248799a63a7bc52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9abd3fde752b027a8d3ca8255295b8.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
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3卷引用:北京市丰台区2023届高三二模数学试题
2 . 设
为无穷数列,给定正整数
,如果对于任意
,都有
,则称数列
具有性质
.
(1)判断下列两个数列是否具有性质
;(结论不需要证明)
①等差数列
:5,3,1,…;②等比数列
:1,2,4,….
(2)已知数列
具有性质
,
,
,且由该数列所有项组成的集合
,求
的通项公式;
(3)若既具有性质
又具有性质
的数列
一定是等差数列,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feaf51b5fdc0b7aad38b26f57825712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575e42a3bdb429360418e949bd963a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
(1)判断下列两个数列是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
①等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f3e9d115d6290eee217a29dc399cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若既具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee83304e529e6d24ea7ff894bd6d87a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5卷引用:北京市西城区2022-2023学年高二下学期期末考试数学试题
北京市西城区2022-2023学年高二下学期期末考试数学试题(已下线)专题02 等比数列4种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北京专用)(已下线)高二数学下学期期末押题试卷01【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-19
名校
3 . 已知
和
是各项均为正整数的无穷数列,如果同时满足下面两个条件:
①
和
都是递增数列;
②
中任意两个不同的项的和不是
中的项.
则称
被
屏蔽,记作
.
(1)若
,
.
(i)判断
是否成立,并说明理由;
(ii)判断
是否成立,并说明理由.
(2)设
是首项为正偶数,公差是
的无穷等差数列,判断是否存在数列
,使得
.如果存在,写出一个符合要求的数列
;如果不存在,说明理由;
(3)设
是取值于正整数集的无穷递增数列,且对任意正整数
,存在正整数
,使得
.证明:存在数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fef6975d285cabcf6be67c78f30d30.png)
(i)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(ii)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5bb0902c0daf52fe26a78a250b96f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33f575cee1cddd9bbc34dcd592a4e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53442dcf82f93d94f20be6bf2c934cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
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2卷引用:北京市海淀区北大附中2023届高三预科部上学期12月阶段练习数学试题
名校
4 . 已知{
}是公差不为0的无穷等差数列.若对于{
}中任意两项
,
,在{
}中都存在一项
,使得
,则称数列{
}具有性质P.
(1)已知
,判断数列{
},{
}是否具有性质P;
(2)若数列{
}具有性质P,证明:{
}的各项均为整数;
(3)若
,求具有性质P的数列{
}的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4877a6af6f2064a3ba51773238144038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27e98494d259c776f02d40202386909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceacfd0395da804e9fd4878fbd93080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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10卷引用:北京市西城区2021-2022学年高二下学期期末考试数学试题
北京市西城区2021-2022学年高二下学期期末考试数学试题北京市海淀区中央民族大学附属中学2022-2023学年高二下学期期中考试数学试题(已下线)北京市第四中学2023-2024学年高三下学期开学测试数学试卷北京市第六十六中学2023-2024学年高二下学期4月期中质量检测数学试题(已下线)专题02 等比数列4种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北京专用)(已下线)4.2.1-4.2.2 等差数列的概念和通项公式-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)4.2.1等差数列的概念(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)(已下线)4.1 等差数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)模块三 专题2 新定义专练【高二下人教B版】(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-19
名校
5 . 素数又称质数,是指在大于
的自然数中,除了
和它本身以外不再有其他因数的自然数.早在
多年前,欧几里德就在《几何原本》中证明了素数是无限的.在这之后,数学家们不断地探索素数的规律与性质,并取得了显著成果.中国数学家陈景润证明了“
”,即“表达偶数为一个素数及一个不超过两个素数的乘积之和”,成为了哥德巴赫猜想研究上的里程碑,在国际数学界引起了轰动.如何筛选出素数、判断一个数是否为素数,是古老的、基本的,但至今仍受到人们重视的问题.最早的素数筛选法由古希腊的数学家提出.
年,一名印度数学家发明了一种素数筛选法,他构造了一个数表
,具体构造的方法如下:
中位于第
行第
列的数记为
,首项为
且公差为
的等差数列的第
项恰好为
,其中
;
.请同学们阅读以上材料,回答下列问题.
(1)求
;
(2)证明:
;
(3)证明:
①若
在
中,则
不是素数;
②若
不在
中,则
是素数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abb59695562b3a1295a251dc97da700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00860a6a9f7275e3d61e519b63802dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc975755665e2675c150f52821609f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
,具体构造的方法如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c9ee6c50000eef418c6103ecf721dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637ba0eba55f2fe7a0d03555056abdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c5fabeba3f3212955d9e282cd5482b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bbc1c45063bba6f24c99a3e30b9fd5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164ae1d08f223df4fa8df94bad8edd57.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de075cbe45f637a11f53685a018e340a.png)
(3)证明:
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbac458da41f3d58829f20be4781d50d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbac458da41f3d58829f20be4781d50d.png)
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|
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|
4卷引用:北京市门头沟区2022届高三一模数学试题
北京市门头沟区2022届高三一模数学试题北京市第一六一中学2022届高三考前热身训练数学试题(已下线)专题4 “素材创新”类型(已下线)第六篇 数论 专题1 数论中的特殊数 微点2 数论中的特殊数综合训练
6 . 在各项均不为零的数列
中,选取第
项、第
项、…、第
项,其中
,
,若新数列
为等比数列,则称新数列为
的一个长度为
的“等比子列”.已知等差数列
,其各项与公差
均不为零.
(1)若在数列
中,公差
,
,且存在项数为3的“等比子列”,求数列
的通项公式;
(2)若
,数列
为
的一个长度为
的“等比子列”,其中
,公比为
.当
最小时,求
的通项公式;
(3)若公比为
的等比数列
,满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac52d20d7bb3a6631f5035ef18b64c19.png)
,证明:数列
为数列
的“等比子列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27628b047da341c79074ea4aa938ddc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527093b2ec760913d0dccff8a099248b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c5b45ef6860f96dd3f033b456056c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ba164203399725ee3c6d42ba903b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)若在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e234c3ca9dee1ae2a17638010eaf7f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dbd9fd3c51552c29d7c351790bb2404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffcbf641680b1c03802d53984840ab66.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/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbbf4d763f3cbe5a71707bc19c78191.png)
(3)若公比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769fe52ac96348d3b12d23d06d702595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac52d20d7bb3a6631f5035ef18b64c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8eeab42f189f7464a50e44bd29406e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
7 . 已知有限数列
为单调递增数列.若存在等差数列
,对于A中任意一项
,都有
,则称数列A是长为m的
数列.
(1)判断下列数列是否为
数列(直接写出结果):
①数列1,4,5,8;②数列2,4,8,16.
(2)若
,证明:数列a,b,c为
数列;
(3)设M是集合
的子集,且至少有28个元素,证明:M中的元素可以构成一个长为4的
数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78af5020619465dd4f48090d1c27825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588d22323fe2e6666bb7052a5d686b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3acb298edf3a1af4b0c18396e7c453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(1)判断下列数列是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
①数列1,4,5,8;②数列2,4,8,16.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf36a8b0b9303e515cab436d325cd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(3)设M是集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b598d2cc3e2ea8e6a76670b1feecbad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
您最近一年使用:0次
2021-04-22更新
|
1039次组卷
|
6卷引用:北京市通州区2021届高三年级一模数学试题
北京市通州区2021届高三年级一模数学试题北京首师附中2021~2022学年高二上学期1月月考数学试题北京市师大附中2022-2023学年高二上学期数学期末试题北京卷专题18数列(解答题)北京市第九中学2024届高三上学期12月月考数学试题(已下线)4.2.2 等差数列的通项公式(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)