名校
1 . 在等比数列
中,
.
(1)求
的通项公式;
(2)设
,数列
的前
项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76eedb8b626a77f8c26d2995bb37067c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea025149c457a3d5c6e508c82f7907f.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94351ce858fa3f3a09cfadc2d23d7253.png)
您最近一年使用:0次
名校
2 . 在数列
中,
,
,设
.
(1)证明:数列
是等差数列;
(2)求数列
的通项公式;
(3)求数列
的前
项和.
![](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/14c8beec5ace6801ab3507ea83c163dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182f57c43fd1d8fb13161224687c469.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的各项均为正数,前
项和为
,且
.
(1)求证:数列
是等差数列;
(2)设
,求
.
![](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/1845c72eededa02f6c389f914c008541.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1845f5fb0b3623155b262b9d846902d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2018-01-18更新
|
693次组卷
|
3卷引用:【全国百强校】吉林省实验中学2017-2018学年高一下学期期中考试数学试题
名校
解题方法
4 . 已知数列
的前
项和为
,且对任意正整数
,都有
成立.
(1)记
,求数列
的通项公式;
(2)设
,求证:数列
的前
项和
.
![](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/b1a4b22741591eb2b311662329403926.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175005738672c8c1f431aac6333ab94f.png)
![](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/0f94ab37fd4cf76a029effba83be40e1.png)
您最近一年使用:0次
2013·福建·一模
名校
5 . 已知数列{an}满足a1=1,
,其中n∈N*.
(1)设
,求证:数列{bn}是等差数列,并求出{an}的通项公式.
(2)设
,数列{cncn+2}的前n项和为Tn,是否存在正整数m,使得
对于n∈N*,恒成立?若存在,求出m的最小值;若不存在,请说明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cb570b2e190d3a0fc98dd2ec3a7dd7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb3133b7ca679c841508e1f9431ff0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391806a296d261369eb28a74d4bd6e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aba7b2970bad263810840bd0b9ca8fa.png)
您最近一年使用:0次
2017-11-25更新
|
2583次组卷
|
23卷引用:吉林省长春市农安县实验中学2019-2020学年高一下学期期末考试数学试题
吉林省长春市农安县实验中学2019-2020学年高一下学期期末考试数学试题河北省石家庄实验中学2019-2020学年高一下学期4月月考数学试题浙江省温州市苍南县金乡卫城中学2019-2020学年高一下学期第一次月考数学试题(已下线)江西省南昌市南昌十中2019-2020高一下学期返校考试数学试题江西省南昌市第十中学2019-2020学年高一5月摸底考试数学试题(已下线)2013届福建省高三高考压轴理科数学试卷(已下线)2014届浙江省绍兴市第一中学高三上学期期中考试理科数学试卷(已下线)2015届湖南省衡阳市高三上学期五校联考文科数学试卷2015届河北省唐山市一中高三上学期期中考试文科数学试卷山东省青州二中2017-2018学年高二10月月考数学试题湖南省醴陵市第一中学2017-2018学年高二上学期期中考试数学(文)试题山东省临沂市兰山区2017—2018学年高二上学期数学(文)期中考试试题内蒙古巴彦淖尔市第一中学2018届高三12月月考数学(理)试题高中数学人教A版必修5 第二章 数列 2.5.3 数列的应用 (2)2017-2018学年陕西省汉中市汉台中学西乡中学高二上学期期末联考数学(理)试题【校级联考】天津市七校(静海一中、宝坻一中、杨村一中等)2018-2019学年高二上学期期末考试数学试题【市级联考】山东省日照市2017届高三下学期第一次模拟考试数学(理)试题安徽省六安中学2020-2021学年高三上学期第三次月考数学(文)试题(已下线)秘籍07 数列-备战2022年高考数学抢分秘籍(新高考专用)河北省唐山市开滦第二中学2020-2021学年高二上学期期末数学试题天津市蓟州区第一中学2021届高三下学期模拟检测一数学试题重庆市北碚区2022-2023学年高二上学期10月月考数学试题湖南省常德市汉寿县第一中学2024届高三上学期期中数学试题
名校
6 . 已知数列
满足
.
(1)求证:数列
为等比数列,并求数列
的通项公式;
(2)求数列
的前
项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c506b55ea84f3d9a376cb4905c8d286.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019b05bea316a92cf1103e8c70bdbd6f.png)
您最近一年使用:0次
2017-08-17更新
|
1013次组卷
|
2卷引用:吉林省梅河口五中2016-2017学年高一下学期期末考试文数试题
名校
解题方法
7 . 已知数列
,
,满足.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d5cab27eabd53067c84de78b399584.png)
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)若数列
满足
,对一切
都成立,求数列
的通项公式.
![](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/06d5cab27eabd53067c84de78b399584.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](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/9396fb0ce65e74cab581a155c3c3fc98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2017-04-01更新
|
1331次组卷
|
2卷引用:吉林省辽源五中2017-2018学年高一下学期第一次月考数学(文)试题
10-11高一下·吉林长春·期中
解题方法
8 . 已知数列
的前
项和为
,且对于任意
,都有
是
与
的等差中项,
(1)求证:
;
(2)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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d637866200a82ea682bba7da5a9d9f6.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456acf42591409e1b7dc6fe08f4672e4.png)
您最近一年使用:0次
名校
9 . 已知数列
满足
,
,
,其中
.
(1)求证:数列
是等差数列,并求出数列
的通项公式;
(2)设
,求数列
的前n项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cab14eade796cbef480ebc572ea2399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381576e698a46df8c497e6b5f8346ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf4ba0fa4ee3bcc28e2cc60a4d57a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c380ffc39ccad63b15e331040720e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314898d22aaac1e3df0d2e1993829d19.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8046e745e78601ffb2b7c276eb663e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b6eaa1cac42bedb3556255ae38d4e4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c108f901a9f72dc1355fd0fd18ae5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68778f67c1cb5a44d18e6a3537f91e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
您最近一年使用:0次
2017-03-21更新
|
1696次组卷
|
5卷引用:吉林省扶余市第一中学2017-2018学年高一下学期期末考试数学试题
11-12高一下·吉林长春·期中
名校
10 . 已知
是等差数列
的前
项和,且
.
(1)求
;
(2)令
,计算
和
,由此推测数列
是等差数列还是等比数列,证明你的结论.
![](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/0ce3ab3bfad90de88b45fc2c2be09c5b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c1b8eb4382c751dcc16aee786e6865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bc85af36f64be115dd7c5d88fac6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2016-12-01更新
|
616次组卷
|
3卷引用:2011-2012学年吉林省长春外国语学校高一下学期期中考试数学试卷
(已下线)2011-2012学年吉林省长春外国语学校高一下学期期中考试数学试卷【全国市级联考】湖南省武冈市2017-2018学年高二学考模拟数学试题黑龙江省牡丹江市第二高级中学2022-2023学年高二上学期期末数学试题