解题方法
1 . “数列
为等比数列”是“数列
为等差数列”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777a10c5eb77332d03d4f6d5f601189e.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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2022-10-29更新
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4卷引用:山东省日照市2022-2023学年高三上学期11月校际联合考试数学试题
山东省日照市2022-2023学年高三上学期11月校际联合考试数学试题山东省临沂市莒南县莒南第一中学2022-2023学年高三上学期期中数学试题湖南省三湘名校教育联盟2022-2023学年高三上学期第一次大联考数学试题(已下线)第四章 数列单元检测卷(能力提升)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)
2 . 将各项均为正数的数列
中的所有项按每一行比上一行多一项的规律排成数表,如图所示.记表中各行的第一个数
,
,
,
,…构成数列
,各行的最后一个数
,
,
,
,…构成数列
,第
行所有数的和为
.已知数列
是公差为
的等差数列,从第二行起,每一行中的数按照从左到右的顺序成公比为
的等比数列,且
,
,
.则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/3ae5c3ec-00d0-4eb0-bca2-d38dac56fad3.png?resizew=235)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdd7e9cd5d1764bc5de8add15700ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8ae9636dba0484afa198a43a57f51b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1222e112464ab97a9decaef4f768c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531a2c7d30e83714b3ce6f022cd21ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7dd0b179bbbd6655f2dc1e48b0b8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d873e39119690783ef45a58ea7c9f477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af372b87dc4f2c4cf1649dddb89fa38.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/3ae5c3ec-00d0-4eb0-bca2-d38dac56fad3.png?resizew=235)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知数列
满足
,
,则数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c88abd936125401c8d7e3bc21f4396.png)
______ .
![](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/e98fd571f61de05068600bcd487db625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c88abd936125401c8d7e3bc21f4396.png)
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2卷引用:山东省潍坊市(安丘、诸城、高密)三县市2022-2023学年高三10月联考数学试题
4 . 已知数列
中,
,当
时,
.
(1)求数列
的通项公式;
(2)设
,数列
中是否存在最大项与最小项?若存在,求出最大项与最小项;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0b34b621b5cb084ece0c40e6aba45e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b221ad4319d75189bc03da184eb19992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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5 . 视力表是根据视角原理设计的,所谓视角就是由外界物体边缘上的两点在眼结点处所形成的夹角,用
表示,其单位为分.视力表以一分视角(1′)为单位进行设计.我国视力的记录采用“五分记录法”,视力表由14行开口方向各异的正方形“E”形视标所组成,从上到下分别对应视力4.0,4.1,……,5.2,5.3,从上面的第一行开始往下,每一行“E”形视标边长都是下一行“E”形视标边长的
倍,且视力
与视角
的关系式为:
.若某同学的视力是4.0,则其视角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
___________ 分;若视力4.0的视标边长为1,则视力5.0的视标边长为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf2d4c6eb02cd7bff3a861545eae4c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145058926a6ba35d82fd37b872fb4fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
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2卷引用:山东省潍坊五县2022-2023学年高三上学期10月联考数学试题
6 . 若由函数
构造的数列
满足
,
,
,则称
为单位收敛函数.现有下列四个函数:①
;②
;③
;④
.其中所有单位收敛函数的编号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d203f90f92ed9fd1b0f95a19c4e91839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32414bf005401cf15cec135f57389757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0bd44896a19f10e008d960df97786a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c486852b242f59f392fcde373541dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82647fc552106005a4ce8262355f76ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f86957b1d88802b3c52060d7471613a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23a2ecf51fe0fbee6d2b80a0db4ce6d.png)
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名校
解题方法
7 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a8277706ce6db5a3c0cd86f477c832.png)
,若数列
前5项的和为31,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a8277706ce6db5a3c0cd86f477c832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4d1266dc2e6709115b099e98c7e568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
A.8 | B.16 | C.31 | D.32 |
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4卷引用:山东省学情空间2022-2023学年高三上学期10月联合考试数学试题
8 . 已知函数
,将满足
的所有正数
从小到大排成数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576421759c0d0c8b86da9943e891d423.png)
(1)证明:数列
为等比数列;
(2)令
,求数列
的前
项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e065d49b26b4458ea2c59d735eec20f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d226ac1b96e081558204fb0729592d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576421759c0d0c8b86da9943e891d423.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f448ce4abd8d4e342805881d9c41ad2.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bbadc2f303192076fce2fca14b24b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a60fab9ac1eb590b1e3a9b1567f570.png)
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2卷引用:山东省学情空间2022-2023学年高三上学期10月联合考试数学试题
9 . 若对任意的
且
,总存在
,使得
,则称数列
是“
数列”.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2343f82fa2f7c80013944e4dd769ea51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f33ba342460bff245fd860ec2976e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
A.至少存在一个等比数列不是“![]() |
B.至少存在两个常数列为“![]() |
C.若![]() ![]() ![]() ![]() |
D.对任意的![]() ![]() ![]() |
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2022-10-01更新
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4卷引用:山东省2022-2023学年高二10月联合调考数学试题B
解题方法
10 . 记
为等比数列
的前
项和.已知
,且
成等差数列.
(1)求
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/0267c45fb7e0a45709d250b6a6f488b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63ff54643c71a355437642164805bf6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865161b69c82f822e873b8cb1cf453d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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2022-10-01更新
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3卷引用:山东省2022-2023学年高二10月联合调考数学试题B