解题方法
1 . 已知圆C:
,过点
的相互垂直的两条直线分别交圆
于点
和
,则四边形
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f308668d4851884b03c3475dff4ef65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad49a1ed2f8dc1bba0ae9a1714b8fa2.png)
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2 . 已知正项数列
满足:对任意的m,
,都有
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03613e0b43e36e09c63d8890c7f950d1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209591cfb9f8271f5ad48d89f214f22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f42949920904b8be46312deb5a8584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03613e0b43e36e09c63d8890c7f950d1.png)
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3 . 幻方又称为魔方,方阵或厅平方,最早记载于中国公元前500年的春秋时期《大戴礼》中,宋代数学家杨辉称之为纵横图.如图所示,将1,2,3,…,9填入
的方格内,使三行、三列、两对角线的三个数之和都等于15,便得到一个3阶幻方;一般地,将连续的正整数1,2,3,…,
填入
的方格内,使得每行、每列、每条对角线上的数字的和相等,这个正方形就叫做
阶幻方.记
阶幻方的一条对角线上的数字之和为
(如:
),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777d8fccf0cf8b55a68488fe48b78744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/9651204c54475c2e8cda8d0a6eeba177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
4 | 9 | 2 |
3 | 5 | 7 |
8 | 1 | 6 |
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2023-08-05更新
|
340次组卷
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4卷引用:云南师范大学附属中学2023届高三第十次高考适应性考试数学试题
云南师范大学附属中学2023届高三第十次高考适应性考试数学试题云南师大附中2023届高考适应性月考卷(十)数学试题(已下线)考点16 几类特殊的数列模型 2024届高考数学考点总动员【练】(已下线)4.2.2 等差数列的前n项和公式——课后作业(基础版)
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4 . 已知数列
的前8项1,1,2,3,5,10,13,21,令
,则
的最小值点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29f0e8465694368a16cdebab5febfcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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2023-06-04更新
|
733次组卷
|
4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
解题方法
5 . 定义
表示与实数
的距离最近的整数(当
为两相邻整数的算术平均值时,
取较大整数),如
,
,
,
,令函数
,数列
的通项公式为
,其前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36243198e5e20c56399e4ad5ac3c519.png)
______ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79961f23daf67ddd2d60b8236ade5473.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac9f6dd8dfc47f2c207cee942ce9256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac9f6dd8dfc47f2c207cee942ce9256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c863a1149d15924221972a7902b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f12b6880d04877d6e0f0cfcac7046dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fdd25405d126dc6d64035532be6189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad443ea76f7b011b5663e74197ad3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176c04c82f19b7678e1eb8002116e3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07abaa1bfc2178951a55b5510229b03d.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/d36243198e5e20c56399e4ad5ac3c519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79961f23daf67ddd2d60b8236ade5473.png)
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6 . 已知
为等差数列
的前
项和.若
,
,则当
取最小值时,
的值为________ .
![](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/a3a2be522aee0a5b497eee5c1ac28740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4408950a78cc3cd2f8533f6c95da57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-05-20更新
|
933次组卷
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4卷引用:云南省“3+3+3”2023届高三高考备考诊断性联考(三)数学试题
云南省“3+3+3”2023届高三高考备考诊断性联考(三)数学试题河南省信阳高级中学2024届高三6月月考数学试题(已下线)专题08 数列(已下线)第02讲 等差数列及其前n项和(十大题型)(讲义)-2
7 . Farey序列是指把在0到1之间的所有分母不超过
的最简分数及0(视为
)和1(视为:
)按从小到大的顺序排列起来所形成的数列,记作F-n,例如F-4就是
.则F-7的项数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f189b13b1c56edf9b3c57431763f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a37d1152b7b04de7241b25d42740bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5296c0056db0e2b5331c9b9a6d45962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9034799a9823682265db15dbbd14820.png)
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解题方法
8 . 已知数列
的前
项和是
,且
,若
,则称项
为“和谐项”,那么数列
的所有“和谐项”的和为__________ .
![](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/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbf0e6250a60701b2c0ed3892cf3bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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|
462次组卷
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2卷引用:云南省曲靖市2023届高三第二次教学质量监测数学试题
9 . 已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](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/a205a3ca07c706b86fde32945a1692bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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10 . 在数列
中,
,且
,设
,其中
为常数.若
是递减数列,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203df4bea72870c92e3703e1dfa96f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80aa5aa16f9c11656f00b5dc0d4e505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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