名校
解题方法
1 . 已知等差数列
的首项
,公差
,且
,设关于x的不等式
的解集中整数的个数为
.
(1)求数列
的前n项和为
;
(2)若数列满足
,求数列
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/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3de6d314dd71900dc8020bb8ab0362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e45a6bd8de1e37fc3d7f21aac8557e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc704a8c18973da608f429452d60a279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2024-04-08更新
|
373次组卷
|
2卷引用:四川省绵阳中学2024届高三高考适应性考试(一)数学(理科)试题
名校
解题方法
2 . 设数列
的前n项和为
,
,
是公差为1的等差数列.
(1)求
的通项公式;
(2)记
,解关于n的不等式
.
![](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/c5b0da4fcbf9ec484dd9444a18609065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d1e3a06f59a35396aac6e12c5e2ee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbb16b9c05204eff7f0ad025c0c466.png)
您最近一年使用:0次
解题方法
3 . 已知数列
满足
.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)若
,数列
的前
项和为
,则关于正整数
的不等式
(其中
)最多有几个解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2279dad9128614e32e1b3446fbf336b7.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebc391558f07f7f484df93950fc6cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
是等差数列,
是等比数列,
.
(1)求
的通项公式;
(2)求数列
的前
项和
,并求不等式
解的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b915c46cbc73bc152844f6f03ca075ba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.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/5737f1f9cad2471f3ca53241b25a1eb9.png)
您最近一年使用:0次
5 . 将2024表示成5个正整数
,
,
,
,
之和,得到方程
①,称五元有序数组
为方程①的解,对于上述的五元有序数组
,当
时,若
,则称
是
密集的一组解.
(1)方程①是否存在一组解
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26725aac8b4a6bf2052893147177a472.png)
等于同一常数?若存在,请求出该常数;若不存在,请说明理由;
(2)方程①的解中共有多少组是
密集的?
(3)记
,问
是否存在最小值?若存在,请求出
的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9b42973c53907f09f2de384c42fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73533ed62f52983da9c3f47e0e84d1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c6ecc1d55a020c1c5105b1c5118730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df660c0848f32943b63bbe22189611be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d2f074101ec58868493992814a2ff9.png)
(1)方程①是否存在一组解
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26725aac8b4a6bf2052893147177a472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19482c76310dc031696d73de0894016.png)
(2)方程①的解中共有多少组是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d91750d298e9d685b9eacb994e7a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2024-03-18更新
|
1213次组卷
|
2卷引用:广东省江门市2024届高三一模考试数学试卷
10-11高二·安徽·期末
名校
解题方法
6 . 已知函数
,且
成等差数列, 点
是函数
图象上任意一点,点
关于原点的对称点
的轨迹是函数
的图象.
(1)解关于
的不等式
;
(2)当
时,总有
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547041bb89115ddf174271b146a63bd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b28f6424fa7fa4048e587416bc8a9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3bfe8f7b456b1fb207618966b1214b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04614d0fac9cde995374a43d4323b723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e20077c8bdf330f4dd21cb570569d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-01更新
|
1123次组卷
|
5卷引用:2010-2011学年安徽省六校教育研究会高二素质测试理科数学
(已下线)2010-2011学年安徽省六校教育研究会高二素质测试理科数学(已下线)2012届上海市徐汇区高三第一学期期中试卷数学(已下线)2012-2013学年江西高安中学高二上期末考试理科数学试卷2016-2017学年辽宁省六校协作体高二下学期期初数学(文)试卷山东省青岛市青岛第二中学2022-2023学年高三上学期12月月考数学试题
7 . 设不等式组
所表示的平面区域为
,记
内的整点个数为
,(整点即横、纵坐标均为整数的点)
(1)计算
的值;
(2)求数列
的通项公式
;
(3)记数列
的前
项和为
,且
,若对于一切的正整数
,总有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc8c4388452ab64b54db55bffa7352b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163e5879f61fdb6bc8771455f40fcbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163e5879f61fdb6bc8771455f40fcbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d064196f38b30602e2c37475c1b59d16.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e811319298c688d1264a792699a5d35.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
(3)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d133c4c47f9746b8d0bee0d24e10f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0f1349bbb967b5b1b1cd13288efaca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
8 . 在①
,②
这两个条件中任选一个补充在下面的问题中,并解知.(注:如果选择多个条件分别解答,按第一个解答计分.)
已知等差数列
的前
项和为
,数列
是正项等比数列,且
,
,______.
(1)求数列
和
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff8f4e4cdb1efa9b30c1741bfac34d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7877d6c39f1b2e5910e69f3813754b.png)
已知等差数列
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad2d7b6d033b3aee7df7703450e6aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed5ef0160bad8913249c4ba1ec2104b.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/ac07953530e3c248b3438fb200fb1661.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
2022-07-02更新
|
795次组卷
|
2卷引用:四川省巴中市2021-2022学年高一下学期期末数学试(文)题
9 . 几位大学生响应国家的创业号召,开发了一款应用软件.为激发大家学习数学的兴趣,他们推出了“解数学题获取软件激活码”的活动.这款软件的激活码为下面数学问题的答案:已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,…,其中第一项是
,接下来的两项是
,
,再接下来的三项是
,
,
,依此类推.求满足如下条件的最小整数N:
且该数列的前N项和为2的整数幂.那么该款软件的激活码是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c851ab8c7c8b2ac92092987a7e32493f.png)
您最近一年使用:0次
2022-09-14更新
|
1154次组卷
|
10卷引用:2019年上海市华东师范大学第二附属中学高三下学期5月信心考三模数学试题
(已下线)2019年上海市华东师范大学第二附属中学高三下学期5月信心考三模数学试题上海市大同中学2017-2018学年高三上学期10月月考数学试题2020届湖南省长沙市长郡中学高三上学期第5次月考数学(文)试题2020届湖南省长沙市长郡中学高三第五次月考数学(文)试题四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高二上学期入学考试数学试题辽宁省渤海大学附属高级中学2022-2023学年高三上学期第二次月考数学试题(已下线)专题17 数列(模拟练)福建师范大学附属中学2023届高三上学期第二次月考数学试题(已下线)第三节 等比数列 核心考点集训2024年新高考Ⅰ卷浙大优学靶向精准模拟数学试题(二)
名校
解题方法
10 . 已知函数
(a,b为常数,
),
,且
有唯一的解.
(1)求
的表达式;
(2)记
,且
,证明数列
是等差数列并求出
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ffddac685bc1056fd8f0bc616dd0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d36f8b82978acaef7bd2c90577578f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3100ae0145d424c88cf5cf7c0e394241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
您最近一年使用:0次
2022-05-04更新
|
209次组卷
|
3卷引用:四川省南充市白塔中学2021-2022学年高一下学期期中考试数学(理)试题