名校
解题方法
1 .
为数列
的前
项和满足:
.
(1)设
,证明
是等比数列;
(2)求
.
![](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/f68c466e8bc7621b3523c49a30d1bd55.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e680f28daa101a42903ef44cf6e6894a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2020-05-23更新
|
629次组卷
|
4卷引用:福建省龙岩第一中学2021-2022学年高二上学期开学考试数学试题
名校
解题方法
2 . 已知数列
的前
项和为
,
,若存在两项
,
,使得
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ba1c5bd4befa16725f99a040435823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfaae40629f480827037653562fa87f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-09-10更新
|
703次组卷
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15卷引用:河南省林州市第一中学2021-2022学年高二下学期2月开学考数学(文)试题
河南省林州市第一中学2021-2022学年高二下学期2月开学考数学(文)试题(已下线)第三章+不等式(基础过关)-2020-2021学年高二数学单元测试定心卷(人教版必修5)甘肃省民乐县第一中学2020-2021学年高二上学期期中考试数学(文)试题(已下线)第四章 数列单元测试(巅峰版)课时训练-【新教材优创】突破满分数学之2020课时训练-2021学年高二数学课时训练(人教A版2019选择性必修第二册)江苏省南通市西亭高级中学2020-2021学年高二上学期第二次阶段检测数学试题江西省靖安中学2019-2020学年高二上学期第一次月考数学(理)试题宁夏银川市三沙源上游学校2021-2022学年高二上学期期末考试数学(文)试题【全国百强校】江西省南昌市第二中学2019届高三第六次考试数学(理)试题河北省邢台市第一中学2018-2019学年高一下学期第三次月考数学试题新疆奎屯市第一高级中学2018-2019学年高一下学期期末考试数学(文)试题四川省绵阳市涪城区南山中学2019-2020学年高三上学期11月月考数学(理)试题山东省泰安第二中学2020届高三11月月考数学试题宁夏石嘴山市第三中学2021届高三补习班上学期期中数学(理)试题(已下线)2021届高三数学新高考“8+4+4”小题狂练(29)云南省楚雄实验中学2023届高三上学期12月月考数学试题
12-13高一下·江苏南通·期中
名校
解题方法
3 . 已知数列
的前
项和为
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59557c76432f5350a610400e7ab8d27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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2022-01-15更新
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13卷引用:2020届四川省绵阳中学高二上期入学考试数学理科试题
2020届四川省绵阳中学高二上期入学考试数学理科试题四川省绵阳中学2022-2023学年高二上学期入学考试数学(文)试题2015-2016学年浙江省杭州高中高二上学期期中数学试卷西藏自治区拉萨市拉萨那曲第二高级中学2019-2020学年高二上学期期末数学试题西藏林芝市第一中学2020-2021学年高二下学期期末考试数学(文)试题(已下线)2012-2013学年江苏省启东中学高一下学期期中考试数学试卷北京市东城二十二中2018届高三上学期期中试卷数学(理)试题【全国百强校】辽宁省沈阳市东北育才学校2018届高三第八次模拟考试数学(文)试题【全国百强校】宁夏石嘴山市第三中学2019届高三上学期期中考试数学(文)试题【全国百强校】福建省厦门外国语学校2019届高三11月月考数学(理)试题广东省梅州市2020届高三下学期总复习质检数学(理)试题(已下线)考点20 递推公式求通项(第1课时)讲解-2021年高考数学复习一轮复习笔记(已下线)专题11 数列通项与前n项和-2020年高考数学母题题源全揭秘(浙江专版)
4 . 已知数列
的前
项和为
,且满足
,
.
(1)证明:数列
为等比数列.
(2)若
,数列
的前项和为
,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/7aae67fda1d77302c568c046488eae9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b676fe25050ad4142f94edf6a3fc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
5 . 已知数列
的前
项和为
,
,若存在两项
,使得
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873ff9f061e2856ceeec92533759edf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38727d002035d341cecf5fc7bd95e5c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d760204a261aae858ee3e353882899.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-01-14更新
|
1884次组卷
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9卷引用:黑龙江省牡丹江一中2020-2021学年高二上学期开学测试数学试题
黑龙江省牡丹江一中2020-2021学年高二上学期开学测试数学试题安徽省合肥市庐阳区合肥六中、合肥八中、阜阳一中、淮北一中四校2019-2020学年高二上学期期末数学(文)试题(已下线)第03章+章末复习课(重点练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版必修5)安徽省淮北市树人高级中学2020-2021学年高二上学期期末数学(理)试题苏教版(2019) 选修第一册 一蹴而就 第4章 4.3.3 等比数列的前n项和安徽省合肥市第一中学2020届高三下学期最后一卷文科数学试题(已下线)专题11应用基本不等式求最值的求解策略解题模板(已下线)第26练 基本不等式及其应用-2021年高考数学(文)一轮复习小题必刷安徽省宣城市郎溪县2021届高考仿真模拟考试数学(文)试题
名校
解题方法
6 . 数列
中,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a76fc5c4b88789bdcdd0825765bc4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
您最近一年使用:0次
7 . 设数列
的前
项和为
,已知
,且
.
(1)证明
为等比数列,并求数列
的通项公式;
(2)设
,且
,证明
;
(3)在(2)的条件下,若对于任意的
不等式
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/4babfac12ddc7e9528167e2030f17f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b1b04112db77069cb75ad66501d564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791f51058793fa835edab49469a2293f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ef086014ad851fdf675c79a41809e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
(3)在(2)的条件下,若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5870925c09801c0b785dd88a6c69d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2020-07-22更新
|
2877次组卷
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7卷引用:黑龙江省牡丹江一中2020-2021学年高二上学期开学测试数学试题
黑龙江省牡丹江一中2020-2021学年高二上学期开学测试数学试题(已下线)第四章 数列单元测试(提升卷)-2020-2021学年高二数学新教材单元双测卷(人教A版2019选择性必修第二册)【全国市级联考】四川省宜宾市2017-2018学年高一下学期期末考试数学试题四川省成都市第七中学2018-2019学年高一下学期期中数学试题吉林省长春实验中学2019-2020学年高一6月月考数学(理)试题(已下线)专题19 数列的综合应用-2(已下线)专题5 数列 第2讲 数列通项与求和
名校
解题方法
8 . 已知等差数列
的前
项的和为
,公差
,若
,
,
成等比数列,
;数列
满足:对于任意的
,等式
都成立.
(1)求数列
的通项公式;
(2)证明:数列
是等比数列;
(3)若数列
满足
,试问是否存在正整数
,
(其中
),使
,
,
成等比数列.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a39dabf1d2cb4094bd2178576970d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1908e360b1cff9a7e59a0456e469f6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dba96dddd47d40c9107553b1c51eb6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970bfc7c34b010d8c880e7b51960494a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d4ad9afdd266c6d38421bdfccd45e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b924cf3c2252a73ec6809ca262643f7.png)
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2020-03-25更新
|
426次组卷
|
2卷引用:辽宁师范大学附属中学2019-2020学年高二上学期开学考试数学试题
9 . 已知数列
的前
项和为
,且
对任意
都成立.
(Ⅰ)求
的值;
(Ⅱ)证明数列
是等比数列,并求出数列
的通项公式;
(Ⅲ)设
,求数列
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/3fe95f40a1e521341a31cb2e91f403fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
(Ⅱ)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.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)
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2020-03-09更新
|
1567次组卷
|
4卷引用:湖南省长沙市长郡中学2020-2021学年高二上学期入学考试数学试题
名校
10 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab02ab01dc1ab8c9201dd876286ffd37.png)
(1)证明
是等比数列,
(2)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/ab02ab01dc1ab8c9201dd876286ffd37.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f774872ffec6c34cadeb450cfefdb11e.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
2019-12-28更新
|
3514次组卷
|
8卷引用:黑龙江省哈尔滨师范大学青冈实验中学校2023-2024学年高二下学期开学考试数学试题
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