名校
解题方法
1 . 已知数列
的前
项和为
,且
,
,其中
是不为
的常数.
(1)求
,
;
(2)是否存在实数
,使得
为等比数列.若存在,求出
的值;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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bfba9f0a6eb33773134a281c3c10a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
2 . 已知等差数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)令
,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9c2efeaa72f32ae52f8d09cc9f931a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.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)
您最近一年使用:0次
2022-09-29更新
|
694次组卷
|
4卷引用:浙江省绍兴蕺山外国语学校2022-2023学年高三上学期9月检测数学试题
3 . 已知各项都为正数的数列{an}满足an+1+an=32n,a1=1,
(1)若bn=an-2n,求证:{bn}是等比数列;
(2)求数列{an}的前n项和Sn.
(1)若bn=an-2n,求证:{bn}是等比数列;
(2)求数列{an}的前n项和Sn.
您最近一年使用:0次
2022-07-01更新
|
715次组卷
|
8卷引用:浙江省绍兴蕺山外国语学校2023-2024学年高三上学期9月检测数学试题
浙江省绍兴蕺山外国语学校2023-2024学年高三上学期9月检测数学试题广东省深圳市光明区高级中学2022届高三模拟(一)数学试题江苏省镇江市五校2021-2022学年高二下学期期末数学试题江苏省镇江第一中学2021-2022学年高二下学期期末数学试题(已下线)专题19 等比数列及其求和(讲义)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)专题27 数列求和-4黑龙江省齐齐哈尔市恒昌中学校2022-2023学年高三上学期开学考试数学试题(已下线)第4章 数列(A卷·知识通关练) (2)
4 . 已知数列
中,
,满足
.
(1)求数列
的通项公式;
(2)设
为数列
的前
项和,若不等式
对任意正整数
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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e921b77cddf7c64c68019b6fcb9db0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](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/eaffad1f1445e35d3423c2e6fdb3972f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-01-12更新
|
826次组卷
|
6卷引用:浙江省绍兴市诸暨海亮高级中学2021-2022学年高三上学期1月测试数学试题
浙江省绍兴市诸暨海亮高级中学2021-2022学年高三上学期1月测试数学试题浙江省绍兴市诸暨海亮高级中学2021-2022学年高三上学期选考模拟最后一测数学试题福建省福州市闽侯县第一中学2024届高三上学期10月月考数学试题(已下线)专题19 数列解答题20题-备战2022年高考数学冲刺横向强化精练精讲(新高考专用)(已下线)解密08 数列(讲义)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(浙江专用)浙江省湖州市安吉县天略外国语学校2022届高三上学期期末模拟数学试题
解题方法
5 . 已知等比数列
的前
项和是
,公比
,
,
,
(1)求数列
的通项公式;
(2)数列
满足,
,
,若对任意的正整数
,
恒成立,求实数
的取值范围.
![](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/f71acdb04454c77e1e25ad4f336cccfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66817003979656ce9b1b87f0dbee4e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8531f8725c1c2004a6a227421f91e494.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3795c79a193937d5fbfd150c5c5427e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1712e0936d47c72e0cf1a856223d536d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2022-01-03更新
|
384次组卷
|
2卷引用:浙江省绍兴市诸暨市海亮高级中学2021-2022学年高三上学期12月选考数学试题
解题方法
6 . 已知等差数列
满足:
,
是
和
的等比中项.数列
满足:
..
(1)求数列
和
的通项公式.
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b5e40cd8eb274d01f8e264622129fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a4d332743e481f66b404cfc240a0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e583b78bbbd719f2b90927d6989d46.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4cd66f0d96aafea7256b514a14138e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894c866e0f8dca93c19c5e73c565534b.png)
您最近一年使用:0次
名校
解题方法
7 . 已知等差数列
的公差
,
,且
,
,
成等比数列,数列
满足
.
(1)求
的通项公式;
(2)求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6278d3cc0086c7aab6ac20712c7d0bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3a9bdce3463e57feb19794f56146e0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a27c112387e56c976489fa484c0d48f.png)
您最近一年使用:0次
2020-10-09更新
|
879次组卷
|
3卷引用:浙江省绍兴市越州中学2022-2023学年高三上学期10月学习质量检测数学试题
名校
解题方法
8 . 如图所示,在
的图像下有一系列正三角形
,记
的边长为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/80f99c27-a1eb-43d4-84f9-8261d3c02e5e.png?resizew=226)
(1)求数列
,
的通项公式;
(2)若数列
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15cc4d294a1bf3132ee9c88f0db11b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e984a7242597334e8c50385bd571ab0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa838e7411d5071ee9a14447971b52a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/80f99c27-a1eb-43d4-84f9-8261d3c02e5e.png?resizew=226)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e37c26dc3aa89f02cc1fda60d10ff48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c882317b819bae6ae0914b798f0504e.png)
您最近一年使用:0次
2020-09-15更新
|
629次组卷
|
4卷引用:浙江省绍兴市诸暨中学2020-2021学年高三上学期10月测试数学试题
浙江省绍兴市诸暨中学2020-2021学年高三上学期10月测试数学试题浙江省宁波市宁海中学2020-2021学年高三上学期9月第一次模拟数学试题(已下线)思想04 化归与转化思想 第三篇 思想方法篇(练)-2021年高考二轮复习讲练测(浙江专用)(已下线)专题6-2 数列求和15种类型归纳-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
解题方法
9 . 已知数列
满足
,数列
的前n项和记为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78515a07797b245e751d0937e2cbb875.png)
(1)求数列
的通项表达式.
(2)记
,若
对任意
恒成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78515a07797b245e751d0937e2cbb875.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed0f7f6702f5e4ac370f1abc87e1a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db27a41f5113966700f93994d22aa58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
您最近一年使用:0次
解题方法
10 . 已知正项数列
满足:
.
(1)求证:
是等比数列,并求
的通项公式;
(2)若数列
满足:
,且数列
的前
项和为
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02c86c5c3b76638d0a1628f53c39921.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708aaba5477dbf8ee60f4c153ca601ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f7de6534e371bc49b9086aaecb45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.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