1 . 定义:若无穷数列
满足
是公比为
的等比数列,则称数列
为“
数列”.设数列
中,
.
(1)若
,且数列
为“
数列”,求数列
的通项公式;
(2)若数列
是“
数列”,是否存在正整数
,使得
,若存在,请求出所有满足条件的正整数
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d83f7ab72975f7588724dcd7726cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447c6f91cc9ed460456899214b5b2d7e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab7d59ce066c8f0b346719003f8e28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d83f7ab72975f7588724dcd7726cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a631d6e9b5cc899fba66187a3ac9735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740b2c2f16c129d11e56ef30d5f08bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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2 . 单调递增的等比数列
满足
,且
是
,
等差中项.
(1)设
,求数列
的前n项和
;
(2)若(1)中
满足
对于
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/3692d1cd54aaa7e2321fff5142e5d2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d473bfcc52ebc119430335531488a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6167e15ff5c344afdbebeb6fadb5830c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若(1)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c3b3f2a9eea49b1d7424586649ffe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 设函数
,数列
满足
,若
是等差数列.则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea50744a07c291f0ca686fe8805bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760415f9629beb699f527067c6c7575c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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4 . 已知数列
的前n项和为
.且
,
是公差为
的等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b1ebe94ad16d80a21f7aa20b59458a.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90207deac50fb1606529b49047f990f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47beab88f3c7978932f2e13824d60191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b1ebe94ad16d80a21f7aa20b59458a.png)
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4卷引用:广西2021届高三综合能力测试(CAT)(一)3月联考数学(文)试题
广西2021届高三综合能力测试(CAT)(一)3月联考数学(文)试题广西柳州市2021届高三下学期三模数学(文)试题广西柳州市2021届高三下学期三模数学(理)试题(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-1
解题方法
5 . 已知数列
和
满足
,
,
,
.则
=_______ .
![](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/a87f066219fb69cd05e6189bf6077452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0936ddc154297c06d5bcdb5c156db68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70e2f535e515d2d3dc2554bf95dc191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb18bcef4741825709adb97510b1bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29274a4db0729665763bdef84c9272a3.png)
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|
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13卷引用:广西名校2021届高三上学期第一次高考模拟数学理科试题
广西名校2021届高三上学期第一次高考模拟数学理科试题(已下线)热点08 数列与不等式-2021年高考数学【热点·重点·难点】专练(新高考)(已下线)押第14题 数列小题-备战2021年高考数学(理)临考题号押题(全国卷2)(已下线)考点35 数列的概念与简单表示法-备战2021年高考数学经典小题考前必刷(新高考地区专用)苏教版(2019) 选修第一册 一蹴而就 第4章 单元整合(已下线)4.3.2 等比数列的通项公式(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)(已下线)专题26 数列的通项公式-52023版 湘教版(2019) 选修第一册 过关斩将 第1章 本章复习提升(已下线)4.3.1.1 等比数列的概念(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)第6讲 数列的通项公式的11种题型总结(4)(已下线)第04讲 数列的通项公式(十六大题型)(讲义)-4(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)【练】 专题2 构造数列问题
6 . 已知数列
的前
项和为
,
,对于任意
,都有
,数列
满足
,
,其前3项和为
.
(1)求数列
,
的通项公式;
(2)设数列
,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/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d01192349234828d29918468294a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62027f02b68e93d609fccd105e85fa62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088ccdcaed0d2e7ff63b1776bbc33e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7f5f44e3c9bcf8e2d5c8cf41165375.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65cb93bc1da7afba83b3c73324f05bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2卷引用:广西师范大学附属外国语学校2021-2022学年高二10月月考数学试题
名校
7 . 已知
是数列
的前n项和,若
,数列
的首项
,则
( )
![](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/65b5f83e9ce037d89ad74051c1c0b713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6ee0c8a2aba48c644443698ffd697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78d551e6cc415f570dc7fc49b825cb1.png)
A.![]() | B.![]() | C.2021 | D.![]() |
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2020-09-26更新
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14卷引用:广西南宁市第十中学2020-2021学年高二上学期段考数学试题
广西南宁市第十中学2020-2021学年高二上学期段考数学试题河北省衡水中学2021届全国高三第一次联合考试(全国卷)理数试题安徽省阜阳市太和第一中学2020-2021学年高三上学期开学摸底检测数学(理)试题(已下线)第22练 等差数列-2021年高考数学(理)一轮复习小题必刷(已下线)第四章 数列-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第二册)(已下线)专题13 数列-备战2021年新高考数学纠错笔记 广东省珠海市第二中学2021届考前模拟数学试题吉林省长春市十一高中2020-2021学年高二下学期第三学程考试数学(理)试题(已下线)专题22 二项式定理必刷小题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)黑龙江省绥化市第九中学2021-2022学年高二下学期4月月考数学试题(已下线)第6章 计数原理(新文化与压轴30题专练)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)陕西省延安市第一中学2021-2022学年高二下学期期末理科数学试题专题02等差数列(已下线)专题02 二项式定理+杨辉三角形压轴题(3)
名校
8 . 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)记
,
为数列
的前
项和,若
对任意的正整数n都成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5a301af4d69b456bdc49bc4ddcd489.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ffb5a730f63c06263f86e1dcd14e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4635bab9739e3caea29347aade242e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac097510b27d634ef968986a79d6e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1518ee858653fb4ce4eb1a82a96ccfa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2019-11-14更新
|
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4卷引用:广西南宁三十六中2020-2021学年高二9月份月考数学试题
名校
9 .
为等差数列
的前
项和,且
.记
,其中
表示不超过
的最大整数,如
,则数列
的前
项和为( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69520249567d3e38a683af24e61893c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a70aa10c5078d2ed248500fd13cb752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e8bcf62bf3c171b87da522aed72cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:广西崇左市高级中学2021-2022学年高二上学期阶段检测(一)数学试题
广西崇左市高级中学2021-2022学年高二上学期阶段检测(一)数学试题【全国百强校】黑龙江省双鸭山市第一中学2018-2019学年高一下学期期中考试数学(理)试题(已下线)2019年9月15日 《每日一题》必修5 —— 每周一测广东省阳江市阳春市第一中学2020-2021学年高二上学期第三次月考数学试题
10 . 已知等差数列
的前
项和为
,并且
,
,数列
满足:
,
,记数列
的前
项和为
.
(1)求
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)记集合
,若
的子集个数为
,求实数
的取值范围.
![](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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca2cc2768794136c1e4da47d2f0873e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70245fecd2a7b5b0abf370fd3067b89.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617814975ecaad35b1657323893c6771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2018-07-07更新
|
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2卷引用:【全国百强校】广西南宁市第三中学2017-2018学年高一下学期期末考试数学(文)试题