1 . 已知各项均为正数的数列
的首项
,其前
项和为
,从①
;②
,
;③
中任选一个条件作为已知,并解答下列问题.
(1)求数列
的通项公式;
(2)设
,设数列
的前
项和
,求证:
.
(注:如果选择多个条件分别解答,按第一个解答计分).
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0378a967740b639bf083fefca36b727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d07ea085e190bed813860d492292efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd7f923a032d19e965858d4fdf45771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58693764692ff0194a846f842b780274.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00f934ec9aa1208cb375e7559070880.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/c55e9df52276e2d89c646a0714bbee8f.png)
(注:如果选择多个条件分别解答,按第一个解答计分).
您最近一年使用:0次
2023-08-03更新
|
846次组卷
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5卷引用:云南省2023届高三“云教金榜”N+1联考·冲刺测试数学试题
云南省2023届高三“云教金榜”N+1联考·冲刺测试数学试题(已下线)模块四 专题8 劣构性问题 (基础)(已下线)专题05 数列 第一讲 数列的递推关系(分层练)江西省萍乡市安源中学2022-2023学年高二下学期期末考试数学试题(已下线)第06讲:数列求和 (必刷5大考题+5大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
2 . 在数列
中,
,当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba48360fc1e1823f54f4618d1e6c18c.png)
(1)求证:数列
是等差数列;
(2)设
,数列
的前n项和为
,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba48360fc1e1823f54f4618d1e6c18c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a5fd14e74e24c0030a862283deb33.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4fc63b0e4d1812c71ffde44ff7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的前
项积为
,且
,
.
(1)求证:数列
是等差数列,并且求其通项公式;
(2)证明:
.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5dc2f2e62f4e01cc8cc0aef12f5738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1172b950b3a1212ba0f75bd18bb70823.png)
您最近一年使用:0次
4 . 在数列
中,
,
,数列
是公比不为1的等比数列,
且
,
,
成等差数列.
(1)求数列
与
的通项公式,
(2)若
,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/aa586033b3a927d1c39a9b53ab028b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9632e7e5a6eb0c85cb44940c60618d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e82778985cd2e9f80ca7b7cabb1a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0531242efa7c1474b16415b1fb8c464.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
5 . 设
是正项等差数列,
,且
成等比数列.
(1)求
的通项公式;
(2)记
的前
项和为
,且
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced4e381e8c3336848b8c436dbc584f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118c5bc33aded6d9fd13bb56be33bd4d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](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/18ec386f0f3ddad65efa9fac2d5bc5d0.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
2023-03-08更新
|
782次组卷
|
6卷引用:宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(文)试题
宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(文)试题(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(文)试题(已下线)专题10数列(解答题)河南省郑州励德双语学校2022-2023学年高二下学期4月考试数学试题福建省漳州立人高级中学2022-2023学年高二下学期3月月考数学试题广东省两阳中学2023-2024学年高二下学期月考一数学试题
名校
解题方法
6 . 已知等差数列
的前
项和为
,
,且
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,证明:
.
![](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/4db8c5bcda961978ed480759ed578e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f445779cba5a480c6070a0fc16d6739.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/8050391385b496e9c059201e4f12600a.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/c215db1d8f69757118ad405b78035628.png)
您最近一年使用:0次
2021-04-10更新
|
2691次组卷
|
9卷引用:云南省昆明市2021届“三诊一模”高三复习教学质量检测数学(理)试题
云南省昆明市2021届“三诊一模”高三复习教学质量检测数学(理)试题(已下线)押第17题 数列-备战2021年高考数学(文)临考题号押题(全国卷1)(已下线)二轮拔高卷04-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)云南省曲靖市第二中学2021-2022学年高二下学期期末考试数学试题河北省秦皇岛市青龙满族自治县实验中学2023届高三上学期开学考试数学试题重庆市第八中学2021-2022学年高二上学期期末数学试题湖北省新高考协作体2021-2022学年高二下学期期末模拟考数学试题辽宁省五校(24中、8中、东北育才、省实验、鞍山一中)联考2021-2022学年高二下学期期末数学试题重庆市第七中学校2022-2023学年高二上学期期末模拟数学试题(一)
名校
解题方法
7 . 南宋数学家在《详解九章算法》和《算法通变本末》中提出了一些新的垛积公式,所讨论的高阶等差数列与一般等差数列不同,高阶等差数列中前后两项之差并不相等,但是逐项差数之差或者高次差成等差数列.现有高阶等差数列,其前7项分别为1,2,4,7,11,16,22,则该数列的第20项为( )
A.172 | B.183 | C.191 | D.211 |
您最近一年使用:0次
2022-11-30更新
|
1556次组卷
|
12卷引用:宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题
宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题黑龙江省哈尔滨市第三中学校2022-2023学年高三上学期阶段性测试(三)数学试题河南省顶级名校2022-2023学年高三上学期12月摸底考试数学(理)试题河南省安阳市林州市林虑中学2022-2023学年高三上学期调研(期末)理科数学试题(已下线)专题3 等差数列的判断(证明)方法 微点2 通项公式法、前n项和公式法(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)专题19新文化与创新试题(已下线)专题09数列(选填题)黑龙江省哈尔滨市第三中学校2022-2023学年高三上学期阶段性测试数学试题河南省信阳高级中学2023届高三二轮复习滚动测试8文科数学试题河北省保定市2023届高三上学期期末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
8 . 已知数列
满足
,
.
(1)设
,证明:
是等差数列;
(2)设数列
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c52909d5e77f7a581509556365cffaf.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2022-03-29更新
|
1657次组卷
|
8卷引用:云南省昆明市2022届高三”三诊一模“复习教学质量检测数学(理)试题
名校
解题方法
9 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)设
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/3c7d606ca5ba5acb50884c6ae7f96f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b544320b695bc7bf51ebf56545f0799d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b419a5c728ab4f50d57fb83c7262a2.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-08-22更新
|
1593次组卷
|
3卷引用:云南省昆明市第一中学高中新课标2023届高三第一次摸底测试数学试题
名校
解题方法
10 . 已知各项均为正数的数列
的首项
,其前
项和为
,从①
;②
,且
;③
中任选一个条件作为已知,并解答下列问题.
(1)求数列
的通项公式;
(2)设
,设数列
的前
项和
,证明:
.
(如果选择多个条件分别解答,按第一个解答计分.)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0378a967740b639bf083fefca36b727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd7f923a032d19e965858d4fdf45771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315b41eeea0dbaa395af2474c4ba6acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58693764692ff0194a846f842b780274.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ec386f0f3ddad65efa9fac2d5bc5d0.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/60f64ba0d54562f1116d869910490ccb.png)
(如果选择多个条件分别解答,按第一个解答计分.)
您最近一年使用:0次