1 . 已知正项等比数列
首项为1,且
成等差数列,则
前6项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56aef84207e4ab45b65d687f6af5a111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.31 | B.![]() | C.![]() | D.63 |
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15卷引用:天津市五校联考2021-2022学年高二下学期期末数学试题
天津市五校联考2021-2022学年高二下学期期末数学试题安徽师范大学附属中学2022届高三下学期适应性考试理科数学试题(已下线)第03讲 等比数列及其前n项和 (高频考点—精练)山东省滨州市沾化区实验高级中学2022-2023学年高三上学期10月月考数学试题河南省三门峡市2022-2023学年高三上学期11月月考数学文科试题天津市西青区杨柳青第一中学2022-2023学年高二上学期期末数学试题天津市四校2022-2023学年高二上学期期末联考数学试题天津市四校(杨柳青一中、47中、百中、咸水沽一中)2022-2023学年高二下学期期末联考数学试题河南省三门峡市2022-2023学年高三上学期11月阶段性考试数学(理)试题(已下线)专题18 等差数列及其求和(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)4.3.2 等比数列的前n项和公式(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)黑龙江省大庆市大庆中学2023届高三高考适应性考试数学试题河南省许昌市禹州市高级中学2022-2023学年高二下学期阶段性考试数学试题(已下线)考点5 等比数列的基本量及其性质 2024届高考数学考点总动员(已下线)考点7 等差、等比数列的联姻 2024届高考数学考点总动员【练】
2 . 已知数列
,
,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
.
(ⅰ)求
;
(ⅱ)求
.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc140737bc06e85eeb8185815a848da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161e6bfee24c80834e0f013f5c6da3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c556533e5d1a21895c1dca698d8dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e82fce48347b206a27cf7219e43ffc0.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/1a1f6b5def1728e9fb6efe8320c03fff.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc07e5dcefd63fa3196ca3b73d2e394f.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088933c82db929cef6093c55fa9618f5.png)
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5卷引用:天津市滨海新区塘沽第一中学2022届高三下学期三模数学试题
天津市滨海新区塘沽第一中学2022届高三下学期三模数学试题天津外国语大学附属外国语学校2022-2023学年高三上学期第二次月考数学试题天津市滨海新区塘沽第一中学2022-2023学年高三上学期第二次月考数学试题 (已下线)数学(天津A卷)(已下线)专题25 等比数列及其前n项和-3
3 . 已知等差数列
的前
项和为
,且
,
.数列
为等比数列,且
,
.
(1)求数列
和
的通项公式;
(2)求
.
(3)求证:
.
![](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/ae2e6956e0073cef684fef6a16bead0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f8a1f39f93da249c7af4474016aaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b8821c758c29c8b02bd79425ecbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d193fb24c1a3487dd6a1abc3ba9585f9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6843e922bd7228677740460548a4081.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390d354c7519d1b92f3e6c30780f6f82.png)
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2卷引用:天津市南开中学2022届高三下学期高考前热身练习数学试题
4 . 若等差数列
满足
,则它的前13项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973f8a0c5826197fb6d7e93f804f6547.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:天津市南开区南大奥宇学校2022-2023学年高三上学期第三次月考数学试题
5 . 已知数列
是公比
的等比数列,前三项和为13,且
,
,
恰好分别是等差数列
的第一项,第三项,第五项.
(1)求
和
的通项公式;
(2)已知
,数列
满足
,求数列
的前2n项和
;
(3)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b3175ab6772cd611f9c42771a9467d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c4e8734cf9695378e52862a603900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c910871ff511e1ea952ad66eff1016db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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12卷引用:天津市南开区2022届高三下学期三模数学试题
天津市南开区2022届高三下学期三模数学试题天津市第七中学2022-2023学年高三上学期12月月考数学试题天津市南开区翔宇学校2022-2023学年高三上学期期末数学试题(已下线)专题27 数列求和-2天津市南开大学附属中学2023届高三下学期2月统练(一)数学试题(已下线)天津市南开中学2023届高三下学期第五次月考数学试题天津市滨海新区塘沽第一中学2023-2024学年高二上学期期末数学练习9(已下线)第7讲 数列求和9种常见题型总结 (2)(已下线)专题6-2 数列大题综合18种题型(讲+练)-1(已下线)模块六 专题6 全真拔高模拟2(已下线)数列 求和专题04数列求和(裂项求和)
名校
解题方法
6 . 已知
是等差数列,
是等比数列,且
.
(1)求数列
的通项公式;
(2)记
的前n项和为
,证明:
;
(3)记
,求数列
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/ed708127acc295fc81a11bd041ebc3dc.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66cd196884f1ffbb3b582523edb262ef.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce271faaca45050e14df41e8f0abc6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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名校
解题方法
7 . 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)
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3卷引用:天津市第一中学2022届高三下学期4月第四次月考数学试题
名校
解题方法
8 . 已知
是公差为3的等差数列,
是公比为2的等比数列,且
.
(1)求
和
的通项公式
(2)若数列
满足对于任意的
,且
.
①求
的通项公式;
②数列
满足
,求
.
![](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/e651aa13af7d55a1bebf11791c56764f.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/c97c2b746d7f363c7b3739a46e7a8e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43bb67cf8df57986da087b0b1dd3ffd6.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3341a3b9b1e614a7587e51f3076f084b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785bb3d13678a572f1d43ec6594944b5.png)
您最近一年使用:0次
9 . 已知数列
的首项
,且满足
.
(1)证明数列
是等差数列,并求数列
的通项公式;
(2)求
的值;
(3)设
,数列
的前
项和为
,求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd640958b6bcfcb861cff84fa2fd85b.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6603814ac39b169453607671158d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2484667635625e562d1ab8f04e6a15fc.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da91003904784639595112aabe0c8c8f.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2卷引用:天津市河西区2022届高三下学期总复习质量调查(二)数学试题
10 . 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;
(2)证明数列
是等比数列,并求
的通项公式;
(3)求证:对任意的
,
.
![](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/b575a0ea2701c7c70af06b0a990c5bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3567c3d83d7ee8c3acf5b18d7de0a3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9b0e5214575fdbfbe00302189656f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907fce0e59f19c1dfcad75aceac9572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dafd98e5b223908b13013c3cacc0386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001edf4ac9a0f18758010ba141739a86.png)
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5卷引用:天津市部分区2022届高三下学期质量调查(二)数学试题
天津市部分区2022届高三下学期质量调查(二)数学试题天津市朱唐庄中学2022届高三线上模拟数学试题(已下线)专题26 数列的通项公式 -2(已下线)专题5 数列 第2讲 数列通项与求和(已下线)第6讲 数列的通项公式的11种题型总结(2)