名校
解题方法
1 . 已知公差不为零的等差数列
满足:
,且
是
与
的等比中项.设数列
满足
,则数列
的前
项和
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6257ea2f336f2d06c021b6560248a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be9c9b05fd84ac9256d49a5a553af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23432420e37ec7e6bda07a35999c5495.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/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-08-10更新
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581次组卷
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6卷引用:北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题
北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题黑龙江省哈尔滨市哈工大附中2024届高三上学期期中数学试题北京市第十九中学2023-2024学年高二下学期4月期中考试数学试题北京市育英学校2023届高三6月统一练习(一) 数学试题(已下线)模块一 专题6 数列的通项公式与求和问题(已下线)微专题1 数列综合应用-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)
名校
解题方法
2 . 已知
为数列
的前
项和,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fbcc867f0450ffbd8816ca1d30d430.png)
.
(1)求数列
的通项公式;
(2)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/22fbcc867f0450ffbd8816ca1d30d430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391bd47f0e344b04b4e68dd49820ad00.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdb50cacd8eb999c9398a3ec378b416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-12-21更新
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3108次组卷
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5卷引用:福建省漳州市东山第二中学2023届高三上学期期中数学试题
福建省漳州市东山第二中学2023届高三上学期期中数学试题广东省深圳实验、湛江一中、珠海一中三校2024届高三上学期12月联考数学试题广东省惠州市第一中学2024届高三上学期第四次阶段测试数学试题黑龙江省哈尔滨市德强高级中学2024届高三上学期期末数学试题(已下线)重难点5-1 数列通项公式的求法(8题型+满分技巧+限时检测)
3 . 已知数列满足
,且
.
(1)证明:
是等比数列,并求
的通项公式;
(2)已知数列
满足
,求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0096a7a6412aa57d382e983136f2b6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2517da6066a54438ed740a2485d10ebc.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dc43b8d11d5462e4b525dd7b03bcfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762489bb5adde61d47074082de4ed589.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)
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2023-10-23更新
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5卷引用:江苏省宿迁市沭阳如东中学2023届高三上学期期中数学试题
江苏省宿迁市沭阳如东中学2023届高三上学期期中数学试题广东省广州市空港实验中学2024届高三上学期期中数学试题(已下线)专题08 数列(5大易错点分析+解题模板+举一反三+易错题通关)江苏省扬州市宝应县画川高级中学2024届高三上学期第二次阶段性学情检测数学试题河南省焦作市第十二中学2024届高三上学期11月月考数学试题
4 . 已知数列
的前
项和为
,满足
.
(1)求数列
的通项公式;
(2)记
,
是数列
的前
项和,若对任意的
,不等式
都成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ea31774a6a8880c9e1458b67961259.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d44205f0b1b6be44238cf5a35f7ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0c6f1cfe638bbc7e37702a6aaf8d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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|
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4卷引用:江苏省镇江中学2022-2023学年高二上学期期中数学试题
江苏省镇江中学2022-2023学年高二上学期期中数学试题江苏省苏州市桃坞高级中学2023-2024学年高二上学期期中数学试题(已下线)第五章 数 列 专题4 数列中不等式能成立与恒成立的求参问题江苏省淮安市涟水县第一中学2024届高三上学期12月考试数学试题
5 . 已知等差数列
的前n项和为
,且
.当
时,
.
(1)求数列
的通项公式;
(2)若
,求数列
的前n项和
.
![](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/c57758a4b5ccc993f9995c160b823a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd1c145e2e16f9376ac869a6ecb673d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0914c295f572c98dd043d4f84268934.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98eb4e7a6e93aae3774ea34f070eb8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-05-21更新
|
1831次组卷
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4卷引用:广东省广州市培正中学2022届高三下学期期中数学试题
广东省广州市培正中学2022届高三下学期期中数学试题重庆市2023届高三临门一卷(二) 数学试题吉林省通化市梅河口市第五中学2022-2023学年高二下学期6月月考数学试题(已下线)2023年新课标全国Ⅰ卷数学真题变式题19-22
6 . 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
.
(3)
,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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c377dcff859a83631f011003f390f29c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc78188e7f5a33a1c38f0cd186e33d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f565ab60f20ce3958e9b0b7093cb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
您最近一年使用:0次
名校
解题方法
7 . 已知数列
是递增的等差数列,
,且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)若
,设数列
的前
项和为
,求满足
的
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.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/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94fe46dc2275759b853bae34993032.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/3df968c2121537f9d2188cda8d296add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-09-30更新
|
1037次组卷
|
2卷引用:福建省莆田第三中学2022-2023学年高二上学期期中数学试题
名校
解题方法
8 . 设数列
的各项都为正数,且
.
(1)证明数列
为等差数列;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52f9212238a366d3cda80a6b4032a66.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db850e54a545598c4ea061aa6aed9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-09-30更新
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2611次组卷
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9卷引用:福建省诏安县桥东中学2022-2023学年高二上学期期中考试数学试题
福建省诏安县桥东中学2022-2023学年高二上学期期中考试数学试题甘肃省兰州市教育局第四片区联考2023-2024学年高二上学期期中考试数学试题辽宁省六校协作体2024届高三上学期期中联考数学试题(已下线)广东省广州市第九十七中学2024届高三上学期10月月考数学试题(已下线)第4章 数列 章末题型归纳总结(2)(已下线)第09讲 第四章 数列 章节验收测评卷(综合卷)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)(已下线)热点5-1 等差数列的通项及前n项和(8题型+满分技巧+限时检测)(已下线)第4章 数列单元检测(基础卷)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)(已下线)4.2.2 等差数列的前n项和公式——随堂检测
9 . 已知数列
满足
.等比数列
的公比为3,且
.
(1)求数列
和
的通项公式;
(2)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a2dfb2f0fbfc146975092f364cdd9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61456862e4bcb27909d56c20b6b8584f.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/267055eae7af3a95da0cf1d02ff6fb90.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)
您最近一年使用:0次
2023-09-28更新
|
1334次组卷
|
5卷引用:四川省广安市第二中学校2022-2023学年高三上学期期中考试数学(理)试题
10 . 已知数列
满足
,
,令
,设数列
前
项和为
.
(1)求证:数列
为等差数列;并求数列
的通项公式;
(2)若存在
,使不等式
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/e89bddd9c021a9caccc72cd0189e1ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.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/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3185977be193745f403547d1e9800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c00e421d661234aea679759d5fc64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次