1 . 已知数列
是公差为2的等差数列,其前8项的和为64.数列
是公比大于0的等比数列,
.
(1)求数列
和
的通项公式;
(2)记
,
,求数列
的前
项和
;
(3)记
,
,证明数列
的前
项和
.
![](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/eeb221d1bf9cda5fc8c97023b482f521.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6520989362ddad9f9d934f7de6b2edf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
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786次组卷
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3卷引用:天津市海河中学2022-2023学年高三上学期期末数学试题
名校
解题方法
2 . 已知数列
是各项均不为零的等差数列,
为其前
项和,且
,若不等式
对任意
恒成立,则实数
的最小值是_____________ .
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e11a8123407e15b49abc03b47f91d5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb2c5f869a2c7b1a74cf8bcd0c74819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-01-12更新
|
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2卷引用:天津市新华中学2022-2023学年高二上学期期末数学试题
解题方法
3 . 在等差数列
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ec42a1fb4d702c725f469141866bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
您最近一年使用:0次
4 . 记
是公差不为0的等差数列
的前
项和,已知
,
,数列
满足
,且
.
(1)求
的通项公式,并证明数列
是等比数列;
(2)若数列
满足
,求
的前
项和的最大值、最小值.
(3)求证:对于任意正整数
,
.
![](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/6b106f3aed5e2f23e10c1605045dccbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360d929d12ccfdf847e487cf8eeabf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2669b03c9edf3947bd588e5bb0d800d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9b0e5214575fdbfbe00302189656f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907fce0e59f19c1dfcad75aceac9572b.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ce0d3130c83d0025e1854d63a548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)求证:对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd01dc4ac5ae74f09dddd2882bf3b24.png)
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2022-11-23更新
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1407次组卷
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5卷引用:天津市微山路中学2022-2023学年高三上学期期末数学试题
天津市微山路中学2022-2023学年高三上学期期末数学试题天津市南开中学2022-2023学年高三上学期第二次月考数学试题(已下线)专题05 数列放缩(精讲精练)-1天津市南开中学2023届高三上学期期中数学试题(已下线)专题6-3 数列求和-1
5 . 设{an}是首项为1的等比数列,数列{bn}满足bn=
,已知a1,3a2,9a3成等差数列.
(1)求{an}和{bn}的通项公式;
(2)记Sn和Tn分别为{an}和{bn}的前n项和.证明:Tn<
.
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa3de6486d375096e5b3b8cfe038a90.png)
(1)求{an}和{bn}的通项公式;
(2)记Sn和Tn分别为{an}和{bn}的前n项和.证明:Tn<
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abed851f46886fe48f6bc55316faee7.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca4454314dc1b1727f6c31c6ed8a610.png)
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2022-11-03更新
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995次组卷
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4卷引用:天津市河西区2022-2023学年高三上学期期中数学试题
6 . 已知数列
的各项均为正数,前
项和为
,若
.
(1)求
的通项公式;
(2)设
,数列
的前
项和为
,求证:
;
(3)设
,数列
的前
项和为
,求满足
的最小正整数
的值.
![](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/fce53c8dab20ebaae6a1f0e8391c29e0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da1c77f40f6e4de0202aeac57dd5e2d.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/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7372aefe7ece44fb94fc5f20ce8c4aa.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd0d375c7a5f3d6e322535d413fafe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd82eb43cefa303f054943af5ed5beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-10-27更新
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4卷引用:天津市梧桐中学2022-2023学年高三上学期期末数学试题
7 . 已知等差数列
前
项和为
(
),数列
是等比数列,
,
,
,
.
(1)求数列
和
的通项公式;
(2)若
,设数列
的前
项和为
,求
.
![](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/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab012ccad381f23d7796cd205eaa399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364f8ccb16e0dd0873291c9f351d6ffb.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/56fc0472cdc7b48d71b3dac4d6402a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
您最近一年使用:0次
2024-03-08更新
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1710次组卷
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25卷引用:天津市河西区2021-2022学年高二上学期期末数学试题
天津市河西区2021-2022学年高二上学期期末数学试题辽宁省沈阳市小三校2022-2023学年高三上学期10月月考数学试题(已下线)专题07 数列大题专项训练(已下线)专题07 数列大题专项训练山西省孝义市2018届高三下学期名校最新高考模拟卷(一)数学(文)试题(已下线)专题07+数列大题专项训练-2020-2021学年【补习教材·寒假作业】高二数学(文)(人教A版)(已下线)专题12+数列大题专项训练-2020-2021学年【补习教材·寒假作业】高二数学(人教A版2019)(已下线)专题07+数列大题专项训练-2020-2021学年【补习教材·寒假作业】高二数学(理)(人教A版)(已下线)大题专项训练10:数列(讨论奇偶)-2021届高三数学二轮复习(已下线)专题04 数列综合练习-2020-2021学年高二数学单元复习(人教A版选择性必修第二册)江苏省苏州新草桥中学2023-2024学年高三上学期10月月考数学试题山西省山西大学附属中学2024届高三上学期10月月考(总第四次)数学试题河北省承德市部分高中2024届高三上学期12月期中数学试题河北省部分重点高中2024届高三上学期期中数学试题河南省济源市英才学校2023-2024学年高二上学期10月月考数学试题河南省商丘市第二高级中学2023-2024学年高二上学期12月月考数学试卷 安徽省六安市金寨第一中学2024届高三上学期期末适应性考试数学试题(二)(已下线)专题5-3数列求和及综合大题归类-1广东省佛山市顺德区华侨中学2023-2024学年高二下学期3月月考数学试卷(已下线)第18题 数列不等式变化多端,求和灵活证明方法多(优质好题一题多解)(已下线)第18题 等差等比综合考查,生成数列通项求和(优质好题一题多解)(已下线)第一章数列章末十六种常考题型归类(3)吉林省长春市第八中学2023-2024学年高二下学期第一次月考数学试题辽宁省沈阳市五校协作体2023-2024学年高二下学期期中考试数学试卷(已下线)2024年天津高考数学真题变式题16-20
名校
解题方法
8 . 已知数列
是数列
的前
项和,已知对于任意
,都有
,数列
是等差数列,
,且
成等比数列.
(1)求数列
和
的通项公式.
(2)记
,求数列
的前
项和
.
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6118d99ea5ce8feb86c2edfa9863b78c.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/05ec09a5b5fd94c1dd994a759907ef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6236cfb43def832ee82170a3957976ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccfb41895ec7f30f66ccff2649cab86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3fcf2d55d332154010c79b64692aca.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a46bd27de9efc3438c3ff2561e1c443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3cd79c7edcf79e64ed8d7aec2b9c58.png)
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2022-12-11更新
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917次组卷
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10卷引用:天津市新华中学2022-2023学年高三上学期12月第二次月考数学试题
天津市新华中学2022-2023学年高三上学期12月第二次月考数学试题(已下线)第七章 数列专练10—讨论奇偶(大题)-2022届高三数学一轮复习(已下线)数学-2022年高考押题预测卷02(天津卷)天津外国语大学附属外国语学校2022-2023学年高三上学期期末数学试题天津市滨海新区塘沽第一中学2021届高三下学期第三次模拟考试数学试题(已下线)专题10 数列(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)2021年高考数学押题预测卷(天津卷)01天津市第七中学2021-2022学年高三上学期第一次月考数学试题(已下线)第4章 数列 单元综合检测(难点)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)2021年新高考天津数学高考真题变式题16-20题
名校
9 . 设等差数列
的前n项和为
,
,
.若对任意的正整数n,都有
,则整数k=( )
![](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/b2c7168ac7bd6c804efef6c6e9ebd1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4d4db546d9116ab1a76943178f5058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1280938c18b060b13d513d427e6a322c.png)
A.34 | B.35 | C.18 | D.19 |
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2022-06-07更新
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5卷引用:天津市新华中学2022-2023学年高三上学期月考(一)数学试题
天津市新华中学2022-2023学年高三上学期月考(一)数学试题天津市新华中学2022-2023学年高三上学期第一次月考数学试题河南省部分学校2022届高三下学期5月考前最后一卷文科数学试题青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题(已下线)专题23 求数列前n项和常用方法-2023届高考数学一轮复习精讲精练(新高考专用)
名校
解题方法
10 . 已知
为等差数列,前
项和为
是首项为2的等比数列,且公比大于0,
.
(1)求
和
的通项公式;
(2)若数列
满足:
,求数列
的前
项和
;
(3)若数列
满足:
,证明:
.
![](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/2820b6522600b99f5e01ebd0dbf57df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c3d564acb102c56af306c0c49d9161.png)
(1)求
![](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/8937a87ed89b02577e4ecb4051044165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a340fdd5aaeaaa14d2b5dbb2642ac73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ed618688b3113849ea49b9df7082ef.png)
您最近一年使用:0次
2022-05-23更新
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950次组卷
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3卷引用:天津市新华中学2022届高三下学期5月统练数学试题