1 . 已知数列
前
项和
,点
在函数
的图象上.
(1)求
的通项公式;
(2)设数列
的前
项和为
,不等式
对任意的正整数
恒成立,求实数
的取值范围.
![](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/2cf9462100c8f7caa3339a17b82caace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebff3592f3e44b7e7dd14d5a73488813.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667467e32bbaf18ca017d449b7e22f09.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/a1bb37bacf8c95a66021882c73549e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 已知等差数列{an}的前n项和为Sn,且a3=10,S6=72,bn=
an-30,
(1)求通项公式an;
(2)求数列{bn}的前n项和Tn的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求通项公式an;
(2)求数列{bn}的前n项和Tn的最小值.
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2018-10-05更新
|
2439次组卷
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3卷引用:【市级联考】广东省深圳市高级中学2018-2019学年高二上学期期中考试数学(文)试题
3 . 若数列{an}是的递增等差数列,其中的a3=5,且a1,a2,a5成等比数列,
(1)求{an}的通项公式;
(2)设bn=
,求数列{bn}的前项的和Tn.
(3)是否存在自然数m,使得
<Tn<
对一切n∈N*恒成立?若存在,求出m的值;
若不存在,说明理由.
(1)求{an}的通项公式;
(2)设bn=
![](https://img.xkw.com/dksih/QBM/2017/10/12/1793648458670080/1793732976902144/STEM/62e5320092b64da592270e4b50839e37.png?resizew=123)
(3)是否存在自然数m,使得
![](https://img.xkw.com/dksih/QBM/2017/10/12/1793648458670080/1793732976902144/STEM/68110197a8b34a4e95d99b7604204882.png?resizew=37)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67bd9b440abf3c3741e7ce4d017589ab.png)
若不存在,说明理由.
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2017-10-12更新
|
2177次组卷
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3卷引用:广东省揭阳市普宁华美实验学校2017-2018学年高二上学期第一次月考数学(理)试题
广东省揭阳市普宁华美实验学校2017-2018学年高二上学期第一次月考数学(理)试题广东省梅州市兴宁市第一中学2019-2020学年高三上学期期末数学(文)试题(已下线)专题07 数列与不等式相结合问题(第二篇)-备战2020年高考数学大题精做之解答题题型全覆盖
4 . 设数列
的前
项和为
,
,且对任意正整数
,点
都在直线
上.
(1)求数列
的通项公式;
(2)若
,数列
的前
项和为
,求证:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e89b5a13cba4ed604340409c11df75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9450684ca4c5f6ee21f226f5f40abe2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fee1710ebfcc3027cb8e5bb71e7450.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/2a730cf0bfd4a9f313a4d2c69217433e.png)
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6卷引用:广东省广州市执信中学2018-2019学年高二下学期期中数学(文)试题
真题
名校
5 . 已知数列
满足
,
.
(1)若
为递增数列,且
成等差数列,求
的值;
(2)若
,且
是递增数列,
是递减数列,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dbfa38d09eb8228c1503a374c7ee6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccadf5fe0d8a09ac97324ad2d9f60f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc383c64f1182577bc35c8ec69efd815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd73bb86944362b433be016d442f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
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2016-12-03更新
|
3669次组卷
|
10卷引用:2016-2017学年广东清远三中高二上学期第一次月考数学(理)试卷
2016-2017学年广东清远三中高二上学期第一次月考数学(理)试卷2014年全国普通高等学校招生统一考试理科数学(湖南卷)2015-2016学年安徽省合肥市一六八中高二上开学考试理科数学试卷2018届高三数学训练题(38):等比数列 人教A版 成长计划 必修5 第二章数列 高考链接上海市上海中学2017-2018学年高三下学期5月适应性考试数学试题(已下线)专题17 数列的概念与数列的通项公式-十年(2011-2020)高考真题数学分项(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湖南省常德市第一中学2023届高三下学期第十一次月考数学试题(已下线)专题21 数列解答题(理科)-1
6 . 已知函数
对任意
,都有
.
(1)求
和
的值;
(2)若数列
满足:
则数列
是等差数列吗?请给予证明.
(3)令![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0329244e4c17444ab0ea26d6b7c743d0.png)
,试比较
与
的大小.
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/323e63a3cd874400bda17290ca175694.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/ccc3864712eb47f09f122c7a9e571d08.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/4ceafa0809e94a6fac0cdec887398ed4.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/113449bb8f42489abe72a63359159c94.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f8b1bda9878443baa59f56170a4cb401.png)
(2)若数列
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f2d18a2126324c528a8d1b708c48ee8f.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/5b372179691c41dd95482435d852809f.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f2d18a2126324c528a8d1b708c48ee8f.png)
(3)令
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0329244e4c17444ab0ea26d6b7c743d0.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0c649e2675bd4062979318cb3c8fa332.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/449bb88f84df46aa9f4201ca7c8471cd.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/94028479b758459784068e66b8425212.png)
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2011·广东深圳·二模
7 . 执行下面框图所描述的算法程序,记输出的一列数依次为
,
,…,
,
,
.(注:框图中的赋值符号“
”也可以写成“
”或“:
”)
![](https://img.xkw.com/dksih/QBM/2011/4/28/1570133298298880/1570133303853056/STEM/edaa3c1e9bb643299dde483ca8b5097d.png?resizew=356)
(1)若输入
,写出输出结果;
(2)若输入
,求数列
的通项公式;
(3)若输入
,令
,求常数
(
),使得
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8676904179cba2add222b11be24fc9d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcfc7a450884c5eda2ce6d80688e21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7081ac76e5ac1e22e848eec143578f1c.png)
![](https://img.xkw.com/dksih/QBM/2011/4/28/1570133298298880/1570133303853056/STEM/edaa3c1e9bb643299dde483ca8b5097d.png?resizew=356)
(1)若输入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e260f5fe6e3637a415344ff137c7a6be.png)
(2)若输入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若输入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fce598e15f7e987f25457f07c817c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fddfed51e1f83bd2205e464cc1619c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8ed1627cef9d38bcf5eeb42da84251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2011·广东茂名·一模
8 . 已知数列
满足
,且
.
(Ⅰ)求证:数列
是等差数列,并求通项
;
(Ⅱ)若
,且
,求和
;
(Ⅲ)比较
与
的大小,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2d4ee4ca59ee21a52cdc88b8a7f994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a507879ed62acd7cfec1dbbfe91c1.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d17a1ac79d2fbc8481e319a64c11e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6372af2da3bc6ce6cda193a79a88c975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af884c9717e1584d130525fdda61815.png)
(Ⅲ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855e9b353277395dbfcea8e568182ea.png)
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