名校
解题方法
1 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)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/83ee53ebc6c4d311b7a0277e9b05258b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2 . 写出该数列的一个通项公式
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48042bc6f931bc79b03b6faf033547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2dadbb81280735c96ebd6f6fb5275b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
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名校
解题方法
3 . 已知数列
满足:
,若对任意的
,都有
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/0e2e13b2b3efa4c12979e07ccce87ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9239b86dece8c37e729e1f59b71ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-06-14更新
|
320次组卷
|
2卷引用:上海市建平中学2022-2023学年高一下学期6月月考数学试题
名校
解题方法
4 . 已知等差数列
,前
项和为
,且
.
(1)求数列
的通项公式;
(2)求
的最大值并指出此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dfc2d1f5ff0c47f50c5f5209a0b725.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/19557eeb69331a65fa03fa64c4a41654.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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5 . 若数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa728e297d79590d3686769c7a3fd7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
您最近一年使用:0次
名校
6 . 对于数列
,如果存在一个正整数
,使得对任意的
都有
成立,那么就把这样一类数列
称作周期为
的周期数列,
的最小值称作数列
的最小正周期,以下简称周期.例如当
时
是周期为1的周期数列,当
时
是周期为4的周期数列.
(1)设数列
满足
不同时为0
,求证:数列
是周期为6的周期数列,并求数列
的前2013项的和
;
(2)设数列
的前
项和为
,且
.
①若
,试判断数列
是否为周期数列,并说明理由;
②若
,试判断数列
是否为周期数列,并说明理由;
(3)设数列
满足
,数列
的前
项和为
,试问是否存在
,使对任意的
都有
成立,若存在,求出
的取值范围;不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef65559a6b44930addc23adeb8d854c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126141b8d68abc6a0823fade2f1b8127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082e8fd18cc10f578020188f254a2455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c002bdb39554b14fb5493781924069a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15987d51b64254b36a00be900799d166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](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/e4a67afce3eba3ca099670e3ded418d9.png)
(2)设数列
![](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/5c07ba166ca9af1ffde9dd49876b17a4.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38ac38efc5f58e833f21c725e9711c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29a7d539f5f39eecf615febf9862109.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/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042896d1702c2c0345f21b63d35d766a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
您最近一年使用:0次
名校
7 . 某实验室要在小白鼠身上做连续活体实验.因实验需要,每天晩上做实验消耗其脂肪10克,其脂肪每天增长率为
(从前一次实验后到后一次实验前).设
为第
天
晩上实验后该小白鼠的脂肪含量.第一天晩上实验前测量其脂肪含量为90克,则
.
(1)计算
的值;
(2)写出
的通项公式,并证明你的结论;
(3)为保证实验的有效性,实验前小白鼠的体内脂肪含量应不少于60克.那么该小白鼠某晩是否会因脂肪含量不够而无法进行有效实验吗?若会,是在第几天晩上?若不会,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28555fa2f3a09261cb4e0305d390145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7cc62c0d7a6c7d0a72c8f13c58d609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878d1c268c2f0f83495b88364ae181a4.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)为保证实验的有效性,实验前小白鼠的体内脂肪含量应不少于60克.那么该小白鼠某晩是否会因脂肪含量不够而无法进行有效实验吗?若会,是在第几天晩上?若不会,请说明理由.
您最近一年使用:0次
名校
8 . 在等差数列
中,
,且
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
A.6 | B.7 | C.8 | D.9 |
您最近一年使用:0次
2023-06-14更新
|
399次组卷
|
2卷引用:江西省宜春市宜丰中学2023-2024学年高一下学期3月月考数学试题(创新部)
9 . 已知数列
满足
,
,则( )
![](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/02b0b6e1d022d284f7344a4d1822718c.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2023-05-30更新
|
1006次组卷
|
12卷引用:广东省佛山市南海区南执高级中学2023-2024学年高一下学期第一阶段测数学试题
广东省佛山市南海区南执高级中学2023-2024学年高一下学期第一阶段测数学试题河南省南阳市镇平县第一高级中学2022-2023学年高二下学期5月月考数学试题江苏省南通市海安市实验中学2022-2023学年高二上学期1月月考数学试题江苏省无锡市南菁高级中学2023-2024学年高二上学期9月调研考试数学试题甘肃省张掖市某重点校2023-2024学年高二上学期10月月考数学试题福建省漳州市华安县第一中学2023-2024学年高二上学期第一次(10月)月考数学试题江西省湖口中学2022-2023学年高二下学期5月期中考试数学试题1.3.3 等比数列的前n项和公式(同步练习基础版)广东省汕头市育能实验学校2022-2023学年高二下学期期中数学试题湖南省岳阳市平江县颐华高级中学2023-2024学年高二下学期入学考试数学试题(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)湖北省部分高中联考协作体2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
10 .
内一点O,满足
,则点O称为三角形的布洛卡点.王聪同学对布洛卡点产生兴趣,对其进行探索得到许多正确结论,比如
,请你和他一起解决如下问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/bc3b8703-bfca-4338-83f7-6392d4e710a3.png?resizew=172)
(1)若a,b,c分别是A,B,C的对边,
,证明:
;
(2)在(1)的条件下,若
的周长为4,试把
表示为a的函数
,并求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8c6763a90e0dabdc7df73313a650d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8519a6da07a806c99cf9d5e0ee042d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/bc3b8703-bfca-4338-83f7-6392d4e710a3.png?resizew=172)
(1)若a,b,c分别是A,B,C的对边,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a09b5a76de882bcd5022a3bedb1f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a99bb77a5ec8629e26b0329a8a21db2.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3bf2007903adc64d089a054c2284a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
您最近一年使用:0次
2023-05-12更新
|
1449次组卷
|
5卷引用:重庆市南开中学校2022-2023学年高一下学期第二次月考数学试题
重庆市南开中学校2022-2023学年高一下学期第二次月考数学试题湖北省圆创联考2023届高三下学期五月联合测评数学试题(已下线)第五篇 向量与几何 专题15 几何最值(费马点、布洛卡点等) 微点2 布洛卡点(已下线)重难点突破03 三角形中的范围与最值问题(十七大题型)-3(已下线)专题3 布洛卡点三角形