名校
1 . 在《九章算术》中有一个古典名题“两鼠穿墙”问题:今有垣厚六尺,两鼠对穿.大鼠日一尺,小鼠也日一尺.大鼠日自倍,小鼠日自半,问何日相逢?大意是有厚墙六尺,两只老鼠从墙的两边分别打洞穿墙.大老鼠第一天进一尺,以后每天加倍;小老鼠第一天也进一尺,以后每天减半.问几天后两鼠相遇?( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2017-08-29更新
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1103次组卷
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6卷引用:江西省六校2018届高三上学期第五次联考文数试题
10-11高三·江西新余·阶段练习
名校
解题方法
2 . 已知正项数列
满足:
时,
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,是否存在正整数m,使得对任意的
,
恒成立?若存在,求出所有的正整数m;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dff324ed5585cc045d1b9fe5e96580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1907a914252d133209a982d60a6637.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f83430c694f54c399069add48d1af05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eaeb8d726023f0ea11e9bb426a82dd.png)
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2016-11-30更新
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1751次组卷
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4卷引用:2011届江西省新余四中高三第二次联考数学文卷
(已下线)2011届江西省新余四中高三第二次联考数学文卷2020届湖南省长沙市长郡中学高三月考(六)数学(文)试题河北省衡水市枣强中学2020届高三下学期2月调研数学(文)试题湖北省襄阳市第一中学2022-2023学年高二上学期期末数学试题
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3 . 已知等比数列
的首项是1,公比为3,等差数列
的首项是
,公差为1,把
中的各项按如下规则依次插入
的每相邻两项之间,构成新数列
:
,
,
,
,
,
,
,
,
,
,…,即在
和
两项之间依次插入
中
个项,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ed0224c4aa502c52317eb04b0e7aad.png)
__________ .(用数字作答)
![](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/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fcc69dc28bc11b22f5c9bec9e2aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.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/d7ed0224c4aa502c52317eb04b0e7aad.png)
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2018-05-10更新
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703次组卷
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2卷引用:【全国市级联考】江西省上饶市2018届高三下学期第三次高考模拟考试数学(文)试题
名校
4 . 设数列
,
满足
,
,
,且数列
是等差数列,数列
是等比数列.
(1)求数列
和
的通项公式;
(2)是否存在
,使
,若存在,求出
,若不存在,说明理由.
![](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/1bb88d8831173a3319d95c502110ab31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8592b997d19abf462dfa657056dea220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9a9ec3de6a5e79e9224456ef761212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05946117b44701da227291e10c9f40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7513d87a7458d879211a14c59ec2e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc1efe01d419af89e83ea54b5679b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369111b066c43eade67ac7ffbead2c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2020-02-05更新
|
225次组卷
|
3卷引用:江西省宜春市上高二中2024届高三上学期第六次月考数学试题
12-13高三·上海青浦·期末
名校
5 . 若三个互不相等的实数成等差数列,适当交换这三个数的位置后变成一个等比数列,则此等比数列的公比为 ____________ (写出一个即可).
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2016-12-02更新
|
574次组卷
|
4卷引用:江西省宜春市宜丰县宜丰中学2023-2024学年高三上学期9月月考数学试题
江西省宜春市宜丰县宜丰中学2023-2024学年高三上学期9月月考数学试题(已下线)2013年上海市青浦区高考一模(即期末)数学试卷江苏省镇江中学2022-2023学年高三上学期10月月考数学试题广东省深圳市深圳高级中学(集团)2024届高三下学期适应性考试数学试卷
2013·江西南昌·二模
6 . 已知各项均不相等的等差数列
的前三项和为18,
是一个与
无关的常数,若
恰为等比数列
的前三项,
(1)求
的通项公式.
(2)记数列
,
的前三
项和为
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4140357d6947ea73869e3acb257ae516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df98ce180b9d9e1a83f2c1332e2da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff79c81c77e8252c89bddc8104c4e1cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c522c1c881528ab6f9708f6bdd4c4db5.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/aaaf65af465633678a3ac65236d0de0f.png)
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13-14高三·全国·课后作业
7 . 已知函数f(x)是定义在R上不恒为零的函数,且对于任意实数a,b∈R,满足:f(a·b)=af(b)+bf(a),f(2)=2,an=
(n∈N*),bn=
(n∈N*).
考查下列结论:
①f(0)=f(1);②f(x)为偶函数;
③数列{an}为等比数列;
④数列{bn}为等差数列.
其中正确的结论共有( )
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571592056414208/1571592061820928/STEM/956062f09bbf4b43984802376d14a01a.png)
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571592056414208/1571592061820928/STEM/14e4ef71d9124fc6ad1b24c2a5521f44.png)
考查下列结论:
①f(0)=f(1);②f(x)为偶函数;
③数列{an}为等比数列;
④数列{bn}为等差数列.
其中正确的结论共有( )
A.1个 | B.2个 | C.3个 | D.4个 |
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10-11高三·江西南昌·阶段练习
8 . 无穷数列
的前n项和
,并且
.
(1)求
的值;
(2)求
的通项公式;
(3)作函数
,如果
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a99badd778a7844bd02f5cbb137856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42508dd2bbf426186f64c45c9696626d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)作函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9a8c38c803660c07371b3b794a645d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd651fc0b78659cc40be70754db70b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18276fedc0e03abadbcec011c839f38e.png)
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