1 . 已知数列
:1,
,
,3,3,3,
,
,
,
,
,
,即当
(
)时,
,记
(
).对于
,定义集合
是
的整数倍,
,且
,则集合
中元素的个数为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123374c62330ca2583f96688e9c27005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20fadc7f410eb813783eb020917bd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a9f96597f4006f719b1a14960a8de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ca3befd6622638091e99d273129d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d671d36cfbea49ea92a4f021b46ad162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f302256059aca5d17dcc0fb30eb97a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a055e096a9133737f5f5a67b0249418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d88909e5fcc68bc96d756f2d65060c.png)
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2023-09-25更新
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179次组卷
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4卷引用:湖南省湘西州吉首市2023年第二届中小学生教师解题大赛数学试题
湖南省湘西州吉首市2023年第二届中小学生教师解题大赛数学试题湖南省常德市第一中学2023届高三下学期第十一次月考数学试题(已下线)第03讲 4.2.2等差数列的前 项和公式(3)(已下线)第2讲:复杂数列通项和求和【练】
2 . 设
.在
的方格表的每个小方格中填入区间
中的一个实数.设第
行的总和为
,第
列的总和为
,
.求
的最大值(答案用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f98da45d4de19a962cfa1d186e2755a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ace7d64e7ff100db25a07330654d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba126d3f244b529547fa33b1dc5f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a71c7129333f890292aa75bc1d080a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 求具有下述性质的最小正整数
:若将
中的每个数任意染为红色或者蓝色,则或者存在9个互不相同的红色的数
满足
,或者存在10个互不相同的蓝色的数
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3070b614e81435e29a6571bcf17271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceffa018e8a05505b1b275e97a5c9f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c27ad2066ebe180072945da08f399e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd877ef4c893b656e492c8818822040c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79213177565cc77ba4da1b49e743eb5.png)
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4 . 方程
的最小的20个正实数解之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a34009b48fec4b1bc4a5291274e949.png)
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5 . 在①
,
,
成等比数列,②
,③数列
的前10项和为55.这三个条件中任选一个,补充在下面问题中,并解答问题.
已知等差数列
的前
项和为
,公差
,且__________
(1)求数列
的通项公式;
(2)求数列
的前2023项和.注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359ee9d15f5390bdb02c62855451323c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afca2a021efa9ec2ff31388c198119db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.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/c5c1344592c925b273f2cb9b9e47ebbb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
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名校
6 . 在递减等比数列
中,
,
是方程
的两根,若数列
前
项积为
,则当
取得最大值时,
的值为
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682bf190fe598c0a653026c14dfe256f.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/392a8f641017f5df07890012bd80eec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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7 . 设等差数列
的前
项和为
,
,公差为
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a2be522aee0a5b497eee5c1ac28740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8042f0193d244577d8af2b090050c6c.png)
A.![]() |
B.当![]() ![]() |
C.![]() |
D.使得![]() ![]() |
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解题方法
8 . 各项不为0的数列
满足
,且
.
(1)求证:数列
为等差数列;
(2)若
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea57eca4b72f73d23c3fed1bc61b414a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562bf10d55724c77204c6953c7fbf7e2.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8355941ad1ce719c3164c1c39bd5b448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-03-03更新
|
1657次组卷
|
5卷引用:湖南省湘西州吉首市2023年第二届中小学生教师解题大赛数学试题
9 . 已知
为数列
的前n项和,且
;数列
是各项均为正数的等差数列,
,4,
成等比数列,且
.
(1)求数列
和
的通项公式;
(2)若
,证明
.
![](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/18bb7c1d0429dbea3455011f99013350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a79c23429da6d3e02f63a83541529a3.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/8fab3af5f17a571a697ff0770fd8df2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f43f25cf6e03d904e300e8040bf9d96.png)
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2022-04-24更新
|
820次组卷
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2卷引用:2023年全国中学生数学能力测评(终评)高三年级组试题
名校
10 . 在2022年北京冬奥会开幕式上,二十四节气倒计时惊艳亮相,与节气相配的14句古诗词,将中国人独有的浪漫传达给了全世界.我国古代天文学和数学著作《周髀算经》中记载:一年有二十四个节气,每个节气的晷长损益相同(晷是按照日影测定时刻的仪器,晷长即为所测量影子的长度),二十四节气及晷长变化如图所示,相邻两个节气晷长减少或增加的量相同,周而复始.已知雨水的晷长为9.5尺,立冬的晷长为10.5尺,则冬至所对的晷长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/a1408c76-33ac-473f-90b8-c3aafa2eb592.png?resizew=304)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/a1408c76-33ac-473f-90b8-c3aafa2eb592.png?resizew=304)
A.11.5尺 | B.13.5尺 | C.12.5尺 | D.14.5尺 |
您最近一年使用:0次
2022-04-20更新
|
1562次组卷
|
9卷引用:安徽省太和中学2022-2023学年高二下学期数学竞赛试题
安徽省太和中学2022-2023学年高二下学期数学竞赛试题(已下线)重难专攻(五) 数列中的综合问题 核心考点集训四川省绵阳市2022届高三第三次诊断性考试文科数学试卷四川省绵阳市2022届高三第三次诊断性考试理科数学试题宁夏平罗中学2023届高三(理尖班)上学期第一次月考数学(理)试题陕西省宝鸡市陈仓区虢镇中学2022-2023学年高二上学期期中数学试题(已下线)4.2.1 等差数列的概念 (精讲)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)(已下线)4.2 等差数列(1)(已下线)第4.2.1讲 等差数列的性质及应用(第2课时)-2023-2024学年新高二数学同步精讲精练宝典(人教A版2019选修第二、三册)