1 . 已知集合
,
,将
中所有元素按从小到大的顺序排列构成数列
,设数列
的前n项和为
.
(1)若
,求m的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48dce1bb61745646feb22b0b02ff495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8bcb4837dff168ffe36d82933fb261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.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/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89dda43a251d13dba5ab27174d6ca49.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a901aa78366ac960f5f4e7f1fcbac.png)
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2021-02-07更新
|
1915次组卷
|
7卷引用:湖南省长沙市麓山国际实验学校2022-2023学年高三上学期入学考试数学试题
湖南省长沙市麓山国际实验学校2022-2023学年高三上学期入学考试数学试题江苏省南通市通州区、启东市2020-2021学年高三上学期期末数学试题福建省福州市第一中学2021届高三适应性练习(一)数学试题(已下线)2021年秋季高三数学开学摸底考试卷02(江苏专用)广东省揭阳市揭西县河婆中学2022届高三下学期综合测试(二)数学试题(已下线)模块一 专题5 等差数列与等比数列 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)模块三 专题7 大题分类练(数列)拔高能力练 期末终极研习室(高二人教A版)
2 . 定义:如果一个数列从第2项起,每一项与它前一项的差都大于或等于2,则称这个数列为“D数列”.
(1)若首项为1的等差数列
的每一项均为正整数,且数列
为“D数列”,其前n项和
满足
(
),求数列
的通项公式;
(2)已知等比数列
的每一项均为正整数,且数列
为“D数列”,
,设
(
),试判断数列
是否为“D数列”,并说明理由.
(1)若首项为1的等差数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1546019868f760bbfc1e8ddaea757c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知等比数列
![](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/f2d18186e394aa92257ddc0e644383cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4095513ce0c92852c8ef4008d43c7ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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3 . 已知
均为非负实数,且
.
证明:(1)当
时,
;
(2)对于任意的
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4099e1919c5450fd97590c4858c2d37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81224c37d3740e35f03d6ff902adfe24.png)
证明:(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d48e59fe8e97b6d8323bfe778e7bcc.png)
(2)对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c154ab0e89e6303f44aaeecf959454ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f71ffa702e15a1a7cfd815463d49a2.png)
您最近一年使用:0次
2020-02-25更新
|
306次组卷
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2卷引用:湖南省岳阳市2024届高三下学期考情信息卷数学试题
4 . 已知首项为
的等比数列
的前
项和为
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)对于数列
,若存在一个区间
,均有
,则称
为数列
的“容值区间”.设
,试求数列
的“容值区间”长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.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/04e406b775bbaa0ae52dab5b7bd384a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0b99a3e6cab1cde1bb575f2b228e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a888492710e24e13dcf15448f43e8174.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f144b23a6628703ef1b9546ecd418d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b477cc2b249061d0eb6839114172b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2020-02-15更新
|
872次组卷
|
5卷引用:2020届湖南省长沙市雅礼中学高三第5次月考数学(文)试题
2020届湖南省长沙市雅礼中学高三第5次月考数学(文)试题2020届湖南省娄底市高三上学期期末教学质量检测数学文科试题2020届河南省平顶山市第一中学高三下学期开学检测(线上)文数试题(已下线)专题06 数列中的最值问题(第二篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)第5课时 课后 等比数列的前n项和
5 . 已知首项为
的等比数列
的前
项和为
,且
成等差数列.
(1)求数列
的通项公式;
(2)对于数列
,若存在一个区间
,均有
,则称
为数列
的“容值区间”.设
,试求数列
的“容值区间”长度的最小值.
(注:区间
的长度均为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.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/1e594418151ad532502f71386f52afa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925556107078ba3d2e54463446d10eff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c951b5535dfffd25000700f9147851b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b477cc2b249061d0eb6839114172b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(注:区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac3a650d1725ba387a51de34ac8a7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
您最近一年使用:0次
6 . 设数列
的前
项和为
,若存在非零常数
,使对任意
都有
成立,则称数列
为“和比数列”.
(1)若数列
是首项为
,公比为
的等比数列,判断数列
是否为“和比数列”;
(2)设数列
是首项为
,且各项互不相等的等差数列,若数列
是“和比数列”,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db87ffceab6741bf496f69449cc728d.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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16bbe7bd03d931004b80c38999c1d504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d182ab14fdd9961d62e3188676e58fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db87ffceab6741bf496f69449cc728d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c22ecc1774a69323774bc8ab99dc023.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次