解题方法
1 . 在等差数列
中,已知
,
与
的等差中项为
,等比中项为
,则通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ ;前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065be21c20118f713d288f3a84ad114f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
名校
解题方法
2 . 已知等差数列
中,
,
.
(1)求
的通项公式.
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581b5e9ac80bcfa3c6e7d9377250ee3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92cb410b15fe6fd6e74bf6adb637274f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82ecbca314a76a2cc7ba40066813296.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)
您最近一年使用:0次
名校
解题方法
3 . 数列
有
项,
,对任意
,存在
,若
与前
项中某一项相等,则称
具有性质
.
(1)若
,求
可能的值;
(2)若
不为等差数列,求证:
中存在满足性质
;
(3)若
中恰有三项具有性质
,这三项和为
,使用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccf7e4dc2f2528b70a7b6920a0360de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c439f52fd3e4c4f6c9872041044d7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a45cd3046323db116ec970be533d2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470a3b303d8e0a78a68dde895a46bb88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b07d62c4025696b4c648db0c3dd67bf.png)
您最近一年使用:0次
名校
解题方法
4 . 已知等差数列
满足
,
,数列
满足
.且有
.记
的前n项和为
.
(1)求数列
的通项公式;
(2)若数列
,求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d194ba78838168b0e2dd321063d807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d84ee688592caf22e84910db79e7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bed30336977adc258e3b8c23ad5fdf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0914c295f572c98dd043d4f84268934.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023高二上·江苏·专题练习
解题方法
5 . 已知无穷数列A:
,
满足:①
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed39e20a9dbb75b4b21260d27df85b90.png)
且
;②
,设
为
所能取到的最大值,并记数列
:
,
,….
(1)若数列A为等差数列且
,求其公差d;
(2)若
,求
的值;
(3)若
,
,求数列
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c990e50aad1de332b6f9894634e6acfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed39e20a9dbb75b4b21260d27df85b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eab47e3541d23a4cacac915d4384e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a49997086be2e13a271a4a7b1d4c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9a668c71d17815323b7ec482fd2cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f766f204cf98d973ad5abe03b235e95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8c641c42b6cd7f44c477bbe5761a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7488ed7332650aa2bc908edbd38c05e8.png)
(1)若数列A为等差数列且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7104dd8a81267b6c15ceedcefccfa20.png)
(3)若
![](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/6398ba56f5a708d2d85a02320e1a389d.png)
您最近一年使用:0次
名校
解题方法
6 . 已知两个等差数列2,6,10,
,202及2,8,14,
,200,将这两个等差数列的公共项按从小到大的顺序组成一个新数列,则这个新数列的各项之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
A.1678 | B.1666 | C.1472 | D.1460 |
您最近一年使用:0次
2024-03-03更新
|
722次组卷
|
7卷引用:广东省珠海高新区青鸟北附实验学校2023-2024学年高二上学期第一次月考数学试题
广东省珠海高新区青鸟北附实验学校2023-2024学年高二上学期第一次月考数学试题广东省茂名市信宜市2023-2024学年高二上学期期末数学试题广东省汕尾市陆河县河田中学2023-2024学年高二下学期4月第一次阶段测试数学试题辽宁省沈阳市辽宁实验中学北校2023-2024学年高二下学期4月阶段测试数学试题2024届广东省汕头市普通高考第二次模拟考试数学试题(已下线)专题4 数列中插入项、公共项问题【练】(高二期末压轴专项)(已下线)核心考点1 数列 B提升卷 (高二期末考试必考的10大核心考点)
名校
解题方法
7 . 如图,椭圆
的左右焦点分别为
,
,过
的直线交椭圆于
,
两点,设
,
,
,
,已知
,
,
成等差数列,公差为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c0ad3ad986cbffa1f38262fd762fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152a1df8033d30475929f3f09e7142e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ed9d6eb61c08c2b2e2558701db3f32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df28302dc0f43c539ef20b880ed8409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daffc27e1cb5fed2176ccee2cfbe8792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.![]() ![]() ![]() | B.若![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 设等差数列
的前
项和为
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.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/8ad088f3ec8297e74e50a01e5e76b0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a55aadc0a7cd1b97eced4e34793f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-20更新
|
1328次组卷
|
4卷引用:甘肃省兰州市兰州一中2023-2024学年高二上学期期末数学试题
甘肃省兰州市兰州一中2023-2024学年高二上学期期末数学试题2024年全国普通高中九省联考仿真模拟数学试题(二)(已下线)5.2.2 等差数列的前n项和(3知识点+8题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)江苏省常州市华罗庚中学2024届高三下学期4月冲刺测试一数学试卷
9 . 将数列
中的所有项排成如下数阵:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e481f3de02f0cb0131d63053d37d94b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680a5028252a7cfbef7c99c02e19a529.png)
…
已知从第2行开始每一行比上一行多两项,第1列数
,
,
,…成等差数列,且
,
,从第2行起,每一行中的数按从左到右的顺序均构成以2为公比的等比数列,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e481f3de02f0cb0131d63053d37d94b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680a5028252a7cfbef7c99c02e19a529.png)
…
已知从第2行开始每一行比上一行多两项,第1列数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ab55c0332b6acb1ebf2d79c74348ab.png)
A.![]() |
B.![]() |
C.![]() |
D.若![]() ![]() |
您最近一年使用:0次
2024-01-10更新
|
692次组卷
|
4卷引用:湖南省大联考长沙市一中2024届高三上学期月考数学试卷(五)
湖南省大联考长沙市一中2024届高三上学期月考数学试卷(五)湖南省长沙市第一中学2024届高三上学期月考数学试卷(五)福建省福州市福建师大附中2023-2024学年高二上学期期末考试数学试题(已下线)第8题 数阵问题(一题多变)(压轴小题)
名校
10 . 已知正项等差数列
中,
,其中
,6,
构成等比数列,
,数列
的前
项和为
,若
,不等式
恒成立,则实数
的取值范围为______ .
![](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/7d93c1ae7b22099a5d4c1c4241e5ca18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.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/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d30793e17f7b00abfa51ef3b213ddbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-01-06更新
|
487次组卷
|
5卷引用:广东省珠海市第一中学2024届高三上学期大湾区期末预测数学试题(二)
广东省珠海市第一中学2024届高三上学期大湾区期末预测数学试题(二)山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题湘豫名校联考2023-2024学年高二上学期1月阶段性考试数学试题河南省商丘市第一高级中学2023-2024学年高二上学期1月份半月考数学试卷(已下线)考点6 等比数列的前n项和的性质 2024届高考数学考点总动员【练】