1 . 已知等差数列
的公差为2,且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)若
,求数列
的前
项和
;
(3)在(2)的条件下,
对一切
恒成立,求
最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2753a9aa20b97d3fa24742c3571f0f3.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)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8587989d573a25825a041f82b3a00d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2020-11-14更新
|
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3卷引用:辽宁省沈阳市第一二〇中学2021-2022学年高二下学期第一次月考数学试题
名校
解题方法
2 . (多选题)已知数列
中,前n项和为
,且
,则
的值不可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c010cb8d0922083fb27442d09f15cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d86b081cae9a195fdebe4cd6e6e43e.png)
A.2 | B.5 | C.3 | D.4 |
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2020-10-12更新
|
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4卷引用:辽宁省沈阳市第八十三中学2021-2022学年高二下学期期初考试数学试题
3 . 已知数列
满足
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fc4cbf5d4c01aba36cfa0764de1278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a69c59b22bbb875d664b23ae641e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77288bfa684c2a9ca00c75743232a0e3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知数列
是首项为-6,公差为1的等差数列,数列
满足
且
,则数列
的最大值为_______ .
![](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/241034156168809810395db8604274fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17edf672b95d4821fbc7295c3669527a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6c852d593cb9f6bdfd9eeddb50fa3.png)
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解题方法
5 . 已知数列{an}的通项公式
,则数列{an}的项取最大值时,n=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00130be47f815767a37292e81c44a0c3.png)
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2016-2017学年辽宁庄河高中高二10月考文数试卷2015-2016学年湖南衡阳一中高一下期末数学试卷(已下线)测试卷37 数列(A)-2021届高考数学一轮复习(文理通用)单元过关测试卷(已下线)专题6.1 数列的概念与简单表示法-2021年高考数学(理)一轮复习-题型全归纳与高效训练突破山西省太原市实验中学2021-2022学年高二上学期12月月考数学试题
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解题方法
6 . 已知数列
中,a1=1,其前n项和为
,且满足
.
(1)求数列
的通项公式;
(2)记
,若数列
为递增数列,求λ的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1e1169719d1be83755b8f7a1abb71b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040023578b4d06ef19356208d014fdf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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10卷引用:辽宁省大连市第八中学2022届高三下学期考前最后一次模拟数学试题
辽宁省大连市第八中学2022届高三下学期考前最后一次模拟数学试题2017届河南省洛阳市高三第二次统一考试(3月)数学(理)试卷河北省武邑中学2017届高三下学期一模考试数学(理)试题江苏省南通市启东中学2018-2019学年高一(创新班)上学期期中数学试题2018届内蒙古鄂尔多斯市第一中学高三下学期第四次模拟数学(理)试题2020届江西省南昌市江西师范大学附属中学高三第一次模拟测试卷理科数学人教A版(2019) 选修第二册 突围者 第四章 第一节 数列的概念河南省鹤壁市高中2022-2023学年高二上学期11月居家测试(一)数学试题安徽省滁州市定远县育才学校2021-2022学年高二分层班下学期第二次月考数学试题安徽省滁州市定远县育才学校2021-2022学年高二下学期第一次月考数学试题
名校
7 . 设等比数列
的公比为
,其前
项和为
,前
项之积为
,并且满足条件:
,
,
,下列结论中正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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)
![](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/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0fd8c68054203a659c797f45ed4032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b5524cf67617d7a9d8db51fdca51aa.png)
A.![]() | B.![]() |
C.![]() ![]() | D.数列![]() |
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2019-02-11更新
|
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3卷引用:【市级联考】辽宁省葫芦岛市2018-2019学年高二上学期期末考试 数学(理)试题
11-12高三上·广东茂名·期末
名校
解题方法
8 . 已知数列
是首项为
,公比为
的等比数列,设
,数列
满足
.
(1)求证:
是等差数列;
(2)求数列
的前
项和
;
(3)若
一切正整数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6821eb83c0e78f23cbf124d364ced75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4eabac7b864584927415ff161ada3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eec8c824d00f7f409a8d49599fb6840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-03-21更新
|
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9卷引用:2016-2017学年辽宁东北育才学校高二上期中数学试卷
2016-2017学年辽宁东北育才学校高二上期中数学试卷(已下线)2011届广东省高州市大井中学高三上学期期末考试数学文卷(已下线)2011届江西省六校高三联考数学理卷(已下线)2014届北京市东城区普通校高三上学期期中联考文科数学试卷2014-2015学年湖北省孝感高中高一下学期期末考试数学试卷江西省宜春三中2017-2018学年高二上学期第一次月考数学试题河北省武邑中学2018-2019学年高二上学期期中数学(理)试题(已下线)江西省南昌市南昌十中2019-2020学年高一下学期第一次月考数学试题湖北省武汉市武钢三中2019-2020学年高一下学期期中数学试题
名校
9 . 在各项均为正数的等比数列
中,
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)若数列
满足
,
为数列
的前
项和. 设
,当
最大时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86e2e42b4aa93db9241103e7f61766c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549980ea98031b87af7a207b879d5ba1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d524341a7b48aacd9e695d6dc400b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/8cee7e74da50a77e3655c068a2a10cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2018-11-19更新
|
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2卷引用:【全国百强校】辽宁省沈阳市东北育才学校2018-2019学年高二上学期期中考试数学试题
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10 . 已知函数
的图象经过点
和
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a941fd5008f9ef49e8adad40063b4e.png)
(1)求数列
的通项公式;
(2)设若
,
,
,求
的最小值;
(3)求使不等式
对一切
均成立的最大实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2a119403159f251ca90d8b6f23ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79485e42b7546ccfa3cd6d08491460f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a941fd5008f9ef49e8adad40063b4e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d47456f316f2a761cf3f081decf3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec6a5cb93ba04f2e1b9209f8c4642e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04b7defcd768444d1cce4990548b3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2018-07-14更新
|
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3卷引用:【全国百强校】辽宁省鞍山市第一中学2018-2019学年高二上学期期中考试数学(理)试题