名校
解题方法
1 . 已知
是公差不为零的等差数列,
,且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)求数列
的前n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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da99424678e23edb4e673bc1ae20428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-06-16更新
|
531次组卷
|
19卷引用:内蒙古巴彦淖尔市临河区第三中学2021-2022学年高三(体育班)上学期期末数学试题
内蒙古巴彦淖尔市临河区第三中学2021-2022学年高三(体育班)上学期期末数学试题【全国百强校】内蒙古集宁一中2018-2019学年高二上学期期末考试数学(文)试题【全国百强校】内蒙古集宁一中2018-2019学年高二上学期期末考试数学(理)试题吉林省长春市十一高中2021-2022学年高二下学期第二学程考试数学试题江苏省连云港市2021-2022学年高一上学期期末调研数学试题(4)吉林省长春市第七中学2022-2023学年高二上学期期中数学试题【全国百强校】甘肃静宁县第一中学2017-2018学年高一下学期期末考试数学(理)试题湖南省株洲市醴陵四中2018-2019学年高二下学期期末数学(理)试题甘肃省白银市会宁县第二中学2017-2018学年高二上学期期末数学(文)试题宁夏石嘴山市第三中学2020-2021学年高二上学期第一次月考数学试题山西省朔州市怀仁县大地学校2019-2020学年高一下学期期末数学试题贵州省贵阳市四校2021届高三年级上学期第二次联合考试理科数学试题(已下线)拓展二 数列求和的方法(精讲)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)(已下线)专题4.3 等比数列(A卷基础篇)-2020-2021学年高二数学选择性必修第二册同步单元AB卷(新教材人教A版,浙江专用)湖南省长沙市长郡中学2020-2021学年高二下学期期中数学试题陕西省渭南高级中学2020-2021学年高二上学期期中文科数学试题湖南省常德市第二中学2020-2021学年高二下学期期末数学试题广东省广州科学城中学2022-2023学年高二下学期3月月考数学试题广东省湛江市第七中学2024届高三上学期9月月考数学试题
名校
解题方法
2 . 已知等差数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)若
,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/a90891fac68b7673ea8dc519213d61a2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d448a6edaf0c2fb374c2f640e8e8da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-01-16更新
|
303次组卷
|
4卷引用:内蒙古乌兰浩特市第四中学2022-2023学年高二上学期第三次月考数学(文)试题
3 . 已知数列
满足
,
,
是公差为1的等差数列.
(1)证明:
是等比数列;
(2)求
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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dc43b8d11d5462e4b525dd7b03bcfc.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d363b6982fee3bf1337d1542137a2f3d.png)
(2)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)
您最近一年使用:0次
2022-12-27更新
|
542次组卷
|
3卷引用:内蒙古呼和浩特第二中学2022-2023学年高三上学期12月月考数学文科试题
4 . 已知数列
与
的前
项和分别为
,
,且
,
.
(1)求数列
的通项公式;
(2)
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58fdb7b6c9bc49f57893aa5516afb6b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866eb2dbd7f6fb8a80185dd1582f6ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4640cbcf3a1fe9c86dadc28cba23df72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2022-12-06更新
|
727次组卷
|
4卷引用:内蒙古自治区鄂尔多斯市2022-2023学年高三上学期期中数学理试题
5 . 已知数列
满足
,
.
(1)求证:数列
是等差数列;
(2)若
且
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9d86ea000b78f8cc58947a0b852566.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e74fcd0b38bb7bbe6f0d8d2d4a256.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fc5ab23f5621156c0289826df21edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf506adfe8cc409627d7c71c9e9222b3.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
2022-11-17更新
|
704次组卷
|
7卷引用:内蒙古自治区兴安盟乌兰浩特市第四中学2022-2023学年高二上学期期中数学试题
6 . 已知
是等差数列
的前
项和,
,
.
(1)求数列
的通项公式;
(2)若
,求
的最小值.
![](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/305beb301b14f28592dee6f32a965240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a98d817993ea57b143b0651a7483197.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937228faf3b035ce9fb607ec96f707f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-11-17更新
|
3768次组卷
|
15卷引用:内蒙古自治区兴安盟乌兰浩特市第四中学2022-2023学年高二上学期期中数学试题
内蒙古自治区兴安盟乌兰浩特市第四中学2022-2023学年高二上学期期中数学试题甘肃省武威市民勤县第一中学2022-2023学年高二上学期期中数学试题河北省邯郸冀南新区育华实验学校2022-2023学年高二上学期期中数学试题重庆市兼善中学2022-2023学年高二上学期第二次阶段考数学试题广东省珠海市斗门区第一中学2022-2023学年高二上学期期末数学试题重庆市万州第二高级中学2023届高三上学期2月月考数学试题甘肃省古浪县第三中学2022-2023学年高二下学期开学考试数学试题重庆市万州第二高级中学2023届高三下学期2月月考数学试题(已下线)拓展三:数列与不等式 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)模块三 专题7 数列--基础夯实练(北师大2019版 高二)(已下线)模块三 专题6 数列--基础夯实练(人教B版高二)福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题河北师范大学附属实验中学2024届高三上学期10月月考数学试题(已下线)4.2.2等差数列的前n项和公式(第2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)河南省三门峡市渑池县第二高级中学2023-2024学年高二下学期4月月考数学试题
解题方法
7 . 已知数列
的前n项和为
,满足
,数列
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eddad34c627086e4bc51dff132f956.png)
(1)求数列
和
的通项公式;
(2)设
,求数列
的前n项和为Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5513854e06c7e78158a2ca5a4734ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eddad34c627086e4bc51dff132f956.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c145ede47d16cc36fa56d2d32ae57c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
您最近一年使用:0次
2022-11-15更新
|
763次组卷
|
2卷引用:内蒙古满洲里市第一中学2022-2023学年高三上学期第一次模拟考试试题理科数学试题
名校
解题方法
8 . 已知等差数列
的前
项和为
,公差
为整数,
,且
成等比数列.
(1)求数列
的通项公式;
(2)设数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
,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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5032706dd285c22e149c675da465d9ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e917d2e497b0245863671d63cd0b15.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa172af12f6033165c5820b31566b4e.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)
您最近一年使用:0次
2022-11-15更新
|
1541次组卷
|
5卷引用:内蒙古满洲里市第一中学2022-2023学年高三上学期第一次模拟考试试题理科数学试题
名校
解题方法
9 . 平面内一动点
到定直线
的距离,是它与定点
的距离的两倍.
(1)求点
的轨迹方程
;
(2)过
点作两条互相垂直的直线
,
(直线
不与
轴垂直).其中,直线
交曲线
于
,
两点,直线
交曲线
于
,
两点,直线
与直线
交于点
,若直线
,
,
的斜率
,
,
构成等差数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b0b7dc61346c291554562762fd0558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f998f87124daa3d26643725676b15c97.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5d04fbdee890603b0b3621037f3c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd6a1d6fab318824426e52464a575e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44368a1c81e2bb3608b412ac0c44f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546a035918f025942ca99b9ffebd8eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
您最近一年使用:0次
2022-10-20更新
|
697次组卷
|
4卷引用:内蒙古自治区赤峰市赤峰二中2022-2023学年高三上学期第二次月考理科月考数学试题
内蒙古自治区赤峰市赤峰二中2022-2023学年高三上学期第二次月考理科月考数学试题贵州省六校联盟2023届高三上学期高考实用性联考(一)数学(理)试题贵州省六校联盟2023届高三上学期高考实用性联考(一)数学(文)试题(已下线)专题32 一类与斜率和、差、商、积问题的探究-1
解题方法
10 . 若正项数列
的前n项和为
,首项
,
点在曲线
上.
(1)求数列
的通项公式
;
(2)设
,
表示数列
的前n项和,若
对
恒成立,求实数m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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3b6012123ba42570997fe84c5a853a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e715696b95de4901d2bf8b0757cdeb6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d005409790b3192705a181b2c8e7dfed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0e01b89b34e1e7490272655ee28cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c39b984e70553acb2da1012e26ba36.png)
您最近一年使用:0次
2022-09-28更新
|
915次组卷
|
6卷引用:内蒙古自治区鄂尔多斯市2022-2023学年高三上学期期中数学(文)试题
内蒙古自治区鄂尔多斯市2022-2023学年高三上学期期中数学(文)试题江西省瑞金市第三中学2023届高三上学期阶段性检测二数学(理)试题河南省信阳市商城县2018-2019学年高二上学期期中数学理科试题河南省信阳市商城县2018-2019学年高二上学期期中数学文科试题(已下线)专题05 数列的通项公式(2)(已下线)第7讲 数列求和9种常见题型总结 (2)