1 . 若一个数列的第
项等于这个数列的前
项的乘积,则称该数列为“
积数列”.若各项均为正数的等比数列
是一个“2020积数列”,且
,则当其前
项的乘积取最大值时,
的值为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2021-09-20更新
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5卷引用:专题二检测 数列(练)-2022年高考数学二轮复习讲练测(新教材地区专用)
(已下线)专题二检测 数列(练)-2022年高考数学二轮复习讲练测(新教材地区专用)沪教版(2020) 一轮复习 堂堂清 第四单元 4.7 数列的应用(二)苏教版(2019) 选修第一册 必杀技 第四章 4.3.1 -4.3.2 等比数列(已下线)4.3.1.2 等比数列的性质及应用(练习)-2022-2023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)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)
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2 . 已知等比数列
的首项为
,公比为
,其前
项和为
,下列命题中正确的是______ .(写出全部正确命题的序号)
(1)若等比数列
单调递增,则
,且
;
(2)数列:
,……,也是等比数列;
(3)
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
(2)数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0823466280d29156262ac5ede4f32cf2.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fd0d370fd4a604446d6b74d64cd611.png)
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3 . 等比数列满足如下条件:①
;②数列
单调递增,试写出满足上述所有条件的一个数列的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2021-07-24更新
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8卷引用:北京市西城区2022届高三二模数学试题变式题11-15
(已下线)北京市西城区2022届高三二模数学试题变式题11-15(已下线)专题8 等比数列的单调性 微点1 判断等比数列单调性的方法北京市西城区育才学校2020-2021学年高二下学期期中考试数学试题(已下线)第4讲 等比数列的通项及性质5大题型总结(3)北京交通大学附属中学分校2021-2022学年高二下学期期中数学试题北京市第十九中学2021-2022学年高二下学期期中考试数学试题(已下线)4.3.1 等比数列的概念——课后作业(基础版)(已下线)4.3 等比数列-2021-2022学年高二数学尖子生同步培优题典(苏教版2019选择性必修第一册)
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4 . 等比数列
中,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605496029ea4474ccb4e62e3e5031c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d862bfc4430c9f7352937eae4ac6888e.png)
A.充要条件 | B.必要不充分条件 |
C.充分不必要条件 | D.既不充分也不必要条件 |
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2021-06-05更新
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7卷引用:考点23 等比数列及其前n项和-备战2022年高考数学(理)一轮复习考点帮
(已下线)考点23 等比数列及其前n项和-备战2022年高考数学(理)一轮复习考点帮(已下线)专题1.2 全称量词与存在量词、充要条件(讲)- 2022年高考数学一轮复习讲练测(新教材新高考)1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(理科)试题(十一)江西省赣州市2021届高三二模数学(理)试题江西省九江第一中学2021届高三5月适应性考试数学(理)试题福建省福建师范大学附属中学2021届高三启明级校模拟考试数学试题浙江省温州市瑞安中学2021届高三下学期5月考前适应性考试数学试题
2021·全国·模拟预测
5 . 已知数列
满足:①
,
,;②
,
(
为常数);③
,使得
恒成立.则满足条件的一个数列
的通项公式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057ec4266660f3d99b105a8d4f444f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36338db3cdaf11194eb0d9e29100a457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31abdda89e6bd6a3d58b7a27df1e744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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6 . 对于
有如下4个数列:(1)
;(2)
(3)
(4)
.其中满足条件
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0568d8f3466c37c0067420955d0950b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d422b94b00b4247c3691f7d6bbfc093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c05d5a4cc83b032872bfa145a791e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac801ba48c14d7424cbdf11ea917119b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644a14313da1dfb9475b3e72c85b2bab.png)
A.1 | B.2 | C.3 | D.4 |
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解题方法
7 . 在①
,②
,③
这三个条件中选择一个,补充在下面问题中,并作出解答.
问题:已知数列
的前
项和
,等比数列
的前
项和为
,
,且 ,判断是否存在唯一的
,使得
,且
.若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd87dfcb967adf5607ccbcbf39c2a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c0bbe5276afcab9b9e465d7b504255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3059b69a2e8bbd1e2bbd7621fec14b4.png)
问题:已知数列
![](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/ad7858f272df99862208b526df4473c3.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18156edebadef55784d134dd2cbf1df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5b653a209622a9136a15c3b11b0a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241319266e5c7b2f440db18356f6bcff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcda9dfccd7e7ec90b89ace68154e58d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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8 . 已知等比数列
的首项为
,且
,
,
,
为数列
的前n项和,
为数列
的前n项的积,若
,
中仅有
最小,则实数
的取值范围是( )
![](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/fe9e329f2730b2be926b121f1ae04c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d569cde17c8039dae26157cf6081407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2114a0fe21dc0e5bf831c146ef02b113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-05-28更新
|
832次组卷
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5卷引用:学海导航全国卷大联考2021届高三数学(文)试题
学海导航全国卷大联考2021届高三数学(文)试题学海导航全国卷大联考2021届高三数学(理)试题(已下线)考点6 等比数列的前n项和的性质 2024届高考数学考点总动员【练】1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(理科)试题(十一)辽宁省大连市大连育明高级中学2022-2023学年高二下学期期中数学试题
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9 . 在等比数列{an}中,
且a8>a9,则使得
的自然数n的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e374a7f3882e3aa5a7d3f7acccc965c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9f04105b156af8c5addfe46bfedc0c.png)
A.10 | B.9 | C.8 | D.7 |
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10 . 已知无穷等比数列
满足
,其前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5c8a6c196890aa7871ea0c82061ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.数列![]() | B.数列![]() |
C.数列![]() | D.数列![]() |
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