1 . 已知数列
满足数列
为等比数列,
,
,且对任意的
,
.
(1)求
的通项公式;
(2)
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c548da8d22f8f7e63361f174e788250b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6167e15ff5c344afdbebeb6fadb5830c.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/4e4350dddc7cca2eac5f2671c6ea8370.png)
您最近一年使用:0次
2023-01-18更新
|
590次组卷
|
2卷引用:江西省丰城市第九中学2023届高三复读班下学期开学质量检测数学(文)试题
2 . 已知数列
的首项
,且满足
.
(1)求证:数列
为等比数列;
(2)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335d6a9baa9ce8255920b76a5fc43172.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd4b82cbfc60de4402ec234d03e5641.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf6affbfeeabb9aed95051116b83652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
2023-01-12更新
|
643次组卷
|
3卷引用:江西省丰城中学2023届高三下学期入学考试数学(文)试题
3 . 设数列
的前
项和
满足
(
),且
.
(1)求证:数列
是等比数列;
(2)若
,数列
的前
项和是
,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/f1da18094d96d840176f90c9f7b3cacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f21105d13f6627f936cdc4abc95e035.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/ee6b87b4fd5837f88c01ec0492e62c55.png)
您最近一年使用:0次
2021-08-14更新
|
560次组卷
|
4卷引用:江西省铜鼓中学2020-2021学年高二(实验班)上学期数学(文)试题
4 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4696f990a2bf344ef1bb822fee7135eb.png)
(1)求证:数列
为等比数列,并求出
;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4696f990a2bf344ef1bb822fee7135eb.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f16bed034d9d9a19d0dfc113190d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ef99f92d589ded39087e249553300d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2021-08-17更新
|
453次组卷
|
5卷引用:江西省南昌市豫章中学2021-2022学年高二上学期入学调研(A)数学(理)试题
江西省南昌市豫章中学2021-2022学年高二上学期入学调研(A)数学(理)试题江苏省泰州市泰兴市黄桥中学2020-2021学年高二上学期质量检测(一)数学试题四川省广汉中学洲书院2021-2022学年高一下学期第一次月考数学(理)试题黑龙江省佳木斯市富锦市第一中学2022-2023学年高二上学期期末考试数学试题(已下线)4.3.1等比数列的概念(第1课时)(分层作业)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第二册)
5 . 已知数列
的前
项和是
,且
.
(1)求数列
的通项公式;
(2)设
,求适合方程
的
的值.
![](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/9e71fb238cb6539fa865c84094253f11.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67149239d2bf1674704030eb754892b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0eb6a0454cdf934f9b2c6d608984114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2020-05-31更新
|
648次组卷
|
8卷引用:江西省宜春市宜丰中学2019-2020学年高二下学期开学考试数学(文)试题
江西省宜春市宜丰中学2019-2020学年高二下学期开学考试数学(文)试题(已下线)专题32 数列大题解题模板-2021年高考一轮数学(文)单元复习一遍过(已下线)专题32 数列大题解题模板-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题32 数列大题解题模板-2021年高考一轮数学(理)单元复习一遍过福建省莆田第十五中学2020届高三上学期期中考试数学(理)试题(已下线)专题03 数列大题解题模板-2020-2021学年高二数学单元复习(人教A版选择性必修第二册)云南省陆良县中枢镇第二中学2020-2021学年高二3月月考数学试题辽宁省沈阳市东北育才学校2015-2016学年高三上学期第三次模拟数学试题(理科)
6 . 在庆祝新中国成立七十周年群众游行中,中国女排压轴出场,乘坐“祖国万岁”彩车亮相国庆游行,“女排精神”燃爆中国.某排球俱乐部为让广大排球爱好者体验排球的训练活动,设置了一个“投骰子50米折返跑”的互动小游戏,游戏规则:参与者先进行一次50米的折返跑,从第二次开始,参与者都需要抛掷两枚质地均匀的骰子,用点数决定接下来折返跑的次数,若抛掷两枚骰子所得的点数之和能被3整除,则参与者只需进行一次折返跑,若点数之和不能被3整除,则参与者需要连续进行两次折返跑.记参与者需要做n个折返跑的概率为
.
(1)求
,
,
;
(2)证明
是一个等比数列;
(3)求
,若预测参与者需要做折返跑的次数,你猜奇数还是偶数?试说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383995da400dd95913fb8d2112f23be4.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
2020-05-31更新
|
1249次组卷
|
3卷引用:江西省铅山一中2020-2021学年高二下学期开学考试数学(理)试题
7 . 已知数列
的前
项和为
,
,
,
,则满足
的正整数
的所有取值为__________ .
![](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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3133f4865a479c271b6587ac8e232db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b8849ab41a8c181e92fff1bb5ccdb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-03-18更新
|
314次组卷
|
2卷引用:江西省萍乡市芦溪中学2023届高三上学期开学考数学(文)试题
8 . 已知数列
的前n项和
,且满足
.
(1)求证:数列
是等比数列;
(2)若数列
满足
,
为数列
的前n项和,求证:
.
![](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/ca8ac08b1dda83e8b171d4937c40ce66.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b106d3c1113b9217724bf99d90de3b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2746040b593c449081174b3b5e4920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6828a1cf75f19bb74a0e0490bd65c168.png)
您最近一年使用:0次
2020-04-13更新
|
1181次组卷
|
7卷引用:江西省宜春市宜丰中学2019-2020学年高二下学期开学考试数学(理科)试题
名校
解题方法
9 . 已知数列
的首项
,
,
、
、
.
(1)求证:数列
为等比数列;
(2)记
,若
,求最大正整数
;
(3)是否存在互不相等的正整数
、
、
,使
、
、
成等差数列且
、
、
成等比数列,如果存在,请给出证明;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fa34d5a86d929757c2bc3db1a51e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f92693c8b5e2828929376a6fbb8e638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)是否存在互不相等的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb10dd730b827d3ec05aebe8c18c9e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff1721a696504d02a4c4b20e5ba7f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
您最近一年使用:0次
2020-07-26更新
|
353次组卷
|
10卷引用:江西省抚州市临川第一中学2019-2020学年高一下学期开学考试数学试题
江西省抚州市临川第一中学2019-2020学年高一下学期开学考试数学试题江苏省南通市2019-2020学年高三上学期开学模拟考试数学试题江西省景德镇一中2021-2022学年高一(19)班下学期期中考试数学试题江苏省南通市如皋中学2017-2018学年第一学期高三第二次阶段测试12月数学试题湖南省长沙市长郡中学2019-2020学年高三10月月考数学(理)试题广东省茂名市电白区2018-2019学年高一下学期期中数学试题湖南省长沙市长郡中学2019-2020学年高三上学期第二次月考理科数学试题福建省永泰一中2021届高三上学期数学月考试题(已下线)专题07 《数列》中的最值问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)广东省广州市第十七中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
10 . 已知数列
满足:
,
.
(1)求证:数列
是等比数列;
(2)令
,如果对任意
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca80dd534c780e614e3b5c79a7c243e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8206017831ad08aabddf9d92a2b36b14.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5386447d5703077a1fa4038b0ff767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd624bda9f45309816fc1e6f27e42675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-09-15更新
|
400次组卷
|
12卷引用:江西省南昌市第二中学2020-2021学年高二上学期开学考试数学试题
江西省南昌市第二中学2020-2021学年高二上学期开学考试数学试题江西省新余市第一中学2018届高三毕业班第四次模拟考试数学(理)试题【全国百强校】江西省南昌市第十中学2019届高三上学期第二次月考数学(理)试题【全国百强校】江西省南昌市第十中学2019届高三上学期第二次月考数学(文)试题2014-2015学年广东省揭阳市一中高二下学期第二次段考理科数学试卷【全国百强校】北京市人大附中2019届高三高考信息卷(三)理科数学试题安徽省六安二中河西校区2018-2019学年高三上学期第六次统测文科数学试题2019届湖南省百所重点名校大联考高三高考冲刺数学(理)试题2019届湖南省百所重点名校大联考高三高考冲刺数学(文)试题浙江省湖州中学2020届高三下学期高考模拟测试(一)数学试题河南省南阳市2020-2021学年高三期中质量评估 数学(理)试题河南省南阳市2021届高三上学期期中数学(理科)试题