1 . 已知等差数列
的前n项和为
,且
,
.设
,则
( )
![](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/ae2e6956e0073cef684fef6a16bead0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde13a1d82174255f34cc22f8127787b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff64605bf3f33036c9ef8adab374f123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff5aea5d1d6bcbbf5bdccca43f02c3b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 南宋数学家杨辉在《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,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.如数列1,3,6,10,它的前后两项之差组成新数列2,3,4,新数列2,3,4为等差数列,则数列1,3,6,10被称为二阶等差数列,现有高阶等差数列
、其前7项分别为5,9,17,27,37,45,49,设通项公式
.则下列结论中正确的是( )
(参考公式:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d42cebb4e1b388e8497f9d5594ad2d.png)
(参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a2b1ba86f57af9387eff5d8298cbef.png)
A.数列![]() |
B.数列![]() |
C.![]() |
D.![]() |
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2023-05-18更新
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2卷引用:江苏省无锡市辅仁高级中学2023届高三下学期高考前适应性练习数学试题
名校
3 . 设
为正项等差数列
的前
项和.若
,则
的最小值为( )
![](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/8dd6ed297120e5125ca2c9f3a444bb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7486636b613960ea474c201854ce5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-09更新
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2530次组卷
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9卷引用:江苏省扬州中学2023届高三下学期高考前保温练数学试题
江苏省扬州中学2023届高三下学期高考前保温练数学试题四川省成都市2023届高三三诊理科数学试题广东省华南师范大学附属中学2023届高三三模数学试题广东省东莞市两校2023届高三联合模拟预测数学试题(已下线)第五节 基本不等式B 素养提升卷广东省四校2024届高三上学期10月联考(二)数学试题(已下线)第04讲 基本不等式及其应用(练习)(已下线)高二下学期期末押题卷02-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修)福建省福州第八中学2022-2023学年高二下学期期末考试数学试题
4 . 已知等差数列
满足
,
成等比数列,且公差
,数列
的前n项和为
.
(1)求
;
(2)若数列
满足
,且
,设数列
的前n项和为
,若对任意的
,都有
,求
的取值范围.
![](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/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff65a8d3757f9ee9a2308fbf47cbad.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/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311321ddb16ec24d587d1249b359a821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d9094c09c92610daca8a629d8fb908.png)
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2023-05-08更新
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921次组卷
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3卷引用:江苏省淮安市盱眙中学2023届高三下学期四模数学试题
江苏省淮安市盱眙中学2023届高三下学期四模数学试题山东省淄博实验中学2023届高三第三次模拟考试数学试题(已下线)第08讲 第四章 数列 重点题型章末总结-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)
5 . 大衍数列来源于《乾坤谱》中对易传“大衍之数五十”的推论,主要用于解释中国传统文化中的太极衍生即太极生两仪原理,如图所示(图中
表示太极,
表示阳仪、
表示阴仪).若数列的每一项都代表太极衍生过程中经历过的两仪数量总和,即
为天一对应的经历过的两仪数量总和0,
为衍生到地二时经历过的两仪数量总和2,
为衍生到天三时经历过的两仪数量总和4,…,按此规律,则
为( )
![](https://img.xkw.com/dksih/QBM/2023/5/4/3230607228993536/3231211092058112/STEM/3fb5329fcdc94b64b25ba85a65f4c48d.png?resizew=204)
![](https://img.xkw.com/dksih/QBM/2023/5/4/3230607228993536/3231211092058112/STEM/52623b89a24c418691068a9eab05948f.png?resizew=11)
![](https://img.xkw.com/dksih/QBM/2023/5/4/3230607228993536/3231211092058112/STEM/29f1a466a64f45a48992ba35249b11cc.png?resizew=11)
![](https://img.xkw.com/dksih/QBM/2023/5/4/3230607228993536/3231211092058112/STEM/2e317b518e6042cea4c82f949d6c2cac.png?resizew=11)
![](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/c5bbae9353140c2235610852d04a9a3f.png)
![](https://img.xkw.com/dksih/QBM/2023/5/4/3230607228993536/3231211092058112/STEM/3fb5329fcdc94b64b25ba85a65f4c48d.png?resizew=204)
A.84 | B.98 | C.112 | D.128 |
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6 . 设等差数列{an}的前n项和为Sn,a1≠0,a1+a5=3a2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c87874491239ab5ed184ac4b9f82ff.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c87874491239ab5ed184ac4b9f82ff.png)
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2023-05-05更新
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4卷引用:江苏省七市(南通、泰州、扬州、徐州、淮安、连云港、宿迁)2023届高三三模数学试题
名校
解题方法
7 . 已知等差数列
的各项均为正数,
,
.
(1)求
的前
项和
;
(2)若数列
满足
,
,求
的通项公式.
![](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/d8ebe185ec10781f6dfb96920311aa40.png)
(1)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)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a7c674dd71ec62d991c879727945f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2023-05-05更新
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解题方法
8 . 已知函数
,记等差数列
的前n项和为
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc7f0b8f7d37c06f5ceba1c5875546a.png)
![](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/9c0674ee29ccd53c4c6505b128c8b87e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c922f6200d988fe6afa13659bad783f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857c26a1f96940b6be22b832834b457b.png)
A.![]() | B.![]() | C.2023 | D.4046 |
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2023-04-30更新
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817次组卷
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2卷引用:江苏省镇江中学2023届高三下学期4月(二模)模拟数学试题
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解题方法
9 . 已知数列
的前
项和为
,
,
,若对任意
,等式
恒成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.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/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d353dfa39bda190923877842446dd449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3527ddfb825cc34e68cd1bac9a272a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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2023-04-29更新
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4卷引用:江苏省四校(无锡市辅仁高级中学、江阴高中、宜兴一中、常州市北郊中学)2022-2023学年高三下学期4月阶段性测试数学试题
江苏省四校(无锡市辅仁高级中学、江阴高中、宜兴一中、常州市北郊中学)2022-2023学年高三下学期4月阶段性测试数学试题福建省泉州市安溪铭选中学2024届高三下学期4月质量检测数学试题(已下线)专题2 全真能力模拟2(人教A版)(已下线)专题2 全真能力模拟2(北师大2019版)
10 . 若函数
的定义域为
,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320353121090cb901aebb757fb2d8c9b.png)
___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a5485711386aa0cc3a06cc480656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a3d4e7a86a04cd983481a260e6b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320353121090cb901aebb757fb2d8c9b.png)
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4卷引用:江苏省南通市如皋市2023届高三下学期高考适应性考试(二)数学试题
(已下线)江苏省南通市如皋市2023届高三下学期高考适应性考试(二)数学试题江苏省南通市通州区2023届高三下学期适应性考试(二)数学试题浙江省杭州第二中学2023-2024学年高三上学期第一次月考数学试题 (已下线)专题2-1 函数性质(单调性、奇偶性、中心对称、轴对称、周期性)-2