1 . 已知
为等比数列,
的前
项和为
,前
项积为
,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若数列![]() ![]() |
D.若数列![]() ![]() |
您最近一年使用:0次
2 . 已知数列
满足:
.
(1)求证:数列
是等比数列;
(2)求数列
的通项公式及其前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6fa372f15b2ea0818ae98e0fb0f4fb.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b7d291b36c6723e3bdf69712550e25.png)
(2)求数列
![](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)
您最近一年使用:0次
2023-10-12更新
|
1961次组卷
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14卷引用:上海市杨浦高级中学2022-2023学年高一下学期开学考试数学试题
上海市杨浦高级中学2022-2023学年高一下学期开学考试数学试题上海外国语大学附属外国语学校2022-2023学年高二下学期期中数学试题(已下线)第4章 数列(基础、典型、易错、压轴)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)湖北省荆州市公安县第三中学2022-2023学年高二下学期3月月考数学试题江西省宜春市第三中学2022-2023学年高二下学期期中考试数学试题云南省宣威市第三中学2022-2023学年高二下学期第二次月考数学试题(已下线)模块二 专题1 数列 A基础卷(人教A)黑龙江省宾县第二中学2023-2024学年高三上学期期初学业质量检测数学试题甘肃省白银市白银区大成学校2023-2024学年高二上学期月考(一)数学试题陕西省汉中市2024届高三上学期第二次校际联考模拟预测文科数学试题陕西省汉中市2024届高三上学期第二次校际联考模拟预测理科数学试题江苏省连云港市连云港高级中学2023-2024学年高二上学期期中数学试题山东省菏泽市菏泽外国语学校2023-2024学年高二上学期第二次月考数学试题(已下线)黄金卷04
23-24高二上·上海·课后作业
名校
3 . 下述三个命题中,真命题有( )
命题
:若数列
的前
项和
,则数列
是等比数列;
命题
:若数列
的前
项和
,则数列
是等差数列;
命题
:若数列
的前
项和
,则数列
既是等差数列,又是等比数列.
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/2ed4949895172f0d3acde4e98571ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
命题
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a1bc1b48159ab30e1cb5f9bdc7bd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.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/77c638c720414d182a9f904849764350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
23-24高二上·上海·课后作业
解题方法
4 . 如图所示,有三根针和套在一根针上的若干金属片,按下列规则,把金属片从一根针上全部移到另一根针上.
(1)每次只移动
个金属片;
(2)较大的金属片不能放在较小的金属片上面;
试推测:把
个金属片从
号针移动到
号针,最少需要移动多少次?
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/13/747cb4e0-c189-4e8b-9480-273d40b2417c.png?resizew=168)
(1)每次只移动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)较大的金属片不能放在较小的金属片上面;
试推测:把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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5 . 如图,已知直角三角形
的两直角边
和
的长分别为5和12,直角三角形的斜边
所在的直线与以
、
、…、
、…为圆心,且依次外切的半圆都相切,其中半圆
与边
所在的直线相切,半圆圆心都在边
上,半径分别为
、
、…、
、….
(1)求证:
为等比数列;
(2)求所有半圆弧长的总和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be77704255b3cadb7ae2a66ec35205ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/bb1ff17c-9c09-487d-bd95-ee00041aabac.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfa1350a58d56ecffaac18570fc27d3.png)
(2)求所有半圆弧长的总和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
6 . 设
为等比数列,则“对于任意的
,
”是“
为递减数列”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4afd75f0bca36ab210a25cf572278c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.充分而不必要条件 | B.必要而不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2023-09-01更新
|
942次组卷
|
8卷引用:4.2 等比数列(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)4.2 等比数列(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)安徽省六校教育研究会2024届高三上学期入学素质测试数学试题广东省广州市执信中学2024届高三上学期第二次月考数学试题重庆市第一中学校2023-2024学年高二上学期12月定时练习数学试题四川省眉山市仁寿县第一中学2023-2024学年高二上学期期末模拟考试数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(五)(已下线)4.3.1 等比数列的概念(分层练习)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)专题04 等比数列(十六大题型+过关检测专训)(1)
2023高二下·上海·专题练习
解题方法
7 . 已知数列
各项均为正数,且
,记其前n项和为
.
(1)若数列
为等差数列,
,求数列
的通项公式;
(2)若数列
为等比数列,
,求满足
时,n的最小值.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337668c95e72e6a91588a436fda17b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31a059268c7801f786e93a76d65b68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce6ccf680e0118c2e74586a22c13eda.png)
您最近一年使用:0次
2023高二下·上海·专题练习
解题方法
8 . 在无穷等比数列
中,
,记
,则
等于__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352f99e5e51daa1551167163d5bc5ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68f63b70470c857092ca740cf83a3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda6cdf0b6787bbe783c9fbcf0649f20.png)
您最近一年使用:0次
9 . 由函数确定数列
,
,若函数
的反函数
能确定数列
,
,则称数列
是数列
的“反数列”.
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881767379325c886f9d806ff4fa4ccf3.png)
![](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/034ba25825c13725931c483aa47c9363.png)
(2)对(1)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecaa3a6251533babfaa59450b4ff0fa.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd45ab1f53a00a0a2dd8245ab7d2eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2174394deab39443edad16adb40a652b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023高二下·上海·专题练习
解题方法
10 . 设等比数列
,其中
.
(1)求
的值.
(2)求使
的最小正整数
的值.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd8d0098a86f4b02652bee89bd364f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d04beb6e0df32aa1df928e6fc11e58.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9731f852dded3b2d2e78d83b6f803d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b5a65e6723957cea0bc5f6ddbe4890.png)
您最近一年使用:0次