1 . 等比数列
中,已知
.
(1)求数列
的通项公式;
(2)若
分别为等差数列
的第3项和第5项,试求数列
的通项公式及前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda159a2eefebf8954370f44df0935d9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eedd5b5ba81010aa9f45afbe62fa77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2016-11-30更新
|
8644次组卷
|
50卷引用:天津市红桥区2019-2020学年高二上学期期末数学试题
天津市红桥区2019-2020学年高二上学期期末数学试题(已下线)2011-2012年山东省聊城莘县实验高中高二上学期期中考试数学2016-2017学年河北武邑中学高二文周考11.6数学试卷陕西省西安电子科技中学2017-2018学年高二上学期第一次月考数学试题广西贺州市2017-2018学年高二年级上学期期末质量检测数学(文)试题广西贺州市2017-2018学年高二上学期期末质量检测数学(理)试题陕西省咸阳市旬邑中学、彬州市阳光中学 、彬州中学2019-2020学年高二上学期期中质量检测数学试题江西省新余市第一中学2019-2020学年高二上学期第一次段考数学试题陕西省咸阳市武功县2019-2020学年高二上学期期中数学试题西藏自治区山南市第三高级中学2019-2020学年高二下学期期末考试数学试题广东省广州市西关外国语学校2020-2021学年高二上学期期中数学试题四川省简阳市阳安中学2020-2021学年第一学期高二11月月考数学(理)试题四川省简阳市阳安中学2020-2021学年第一学期高二11月月考数学(文)试题(已下线)专题06 第一章 复习与检测 知识精讲 云南省楚雄天人中学2020-2021学年高二3月月考数学(理)试题天津市北京师范大学天津附属中学2021-2022学年高三上学期第一次月考数学试题福建省宁德市第九中学2021-2022学年高二上学期第一次月考质量检测数学试题河南省南阳市六校2021-2022学年高二上学期第一次联合测试数学(文)试题江苏省西安交通大学苏州附属中学2021-2022学年高二10月份第一次自主检测数学试题甘肃省兰州市教育局第四片区2021-2022学年高二上学期期中考试数学(理)试题山西省太原市英才学校2021-2022学年高二上学期第二次月考数学试题江苏省西安交通大学苏州附属中学2021-2022学年高二上学期10月第一次自主检测数学试题重庆市渝西中学2022-2023学年高二上学期期末数学试题沪教版(2020) 选修第一册 高效课堂 第四章 4.5 复习与小结陕西省西安市铁一中学2023-2024学年高二上学期第二次月考数学试题人教A版(2019) 选修第二册 数学奇书 第四章 数列 章末整合提升四川省宜宾市棠湖高级中学2023-2024学年高二上学期阶段测试三(12月月考)数学试题安徽省六安市毛坦厂中学集团校2023-2024学年高二上学期期末考试数学试题2009年普通高等学校招生全国统一考试文科数学(福建卷)(已下线)2009高考真题汇编3-数列(已下线)新课标高三数学等比数列、数列通项的求法专项训练(河北)(已下线)2011-2012学年江苏省扬州市安宜高级中学高一下期中数学试卷(已下线)2014届四川省成都七中高三二诊模拟理科数学试卷(已下线)2014届四川省成都七中高三二诊模拟文科数学试卷2015届甘肃省兰州市高三诊断考试文科数学试卷2014-2015学年四川省双流县棠湖中学高一下学期期中考试数学试卷2014-2015学年四川省仪陇二中高一下学期6月月考数学试卷【全国市级联考】四川省眉山一中2017-2018学年高一下学期5月月考数学试卷【全国百强校】湖南省长郡中学2019届高三上学期第一次月考(开学考试)数学(文)试题重庆市铜梁一中2019届高三10月月考数学(文)试题(已下线)2020届北京市西城区第四中学高三上学期期中数学试题广东省六校联盟2019-2020学年高三下学期第三次联考数学(文)试题(已下线)题型08 等差数列、等比数列综合问题-2020届秒杀高考数学题型之数列甘肃省静宁县第一中学2020-2021学年高三上学期第三次模拟考试数学(文)试题陕西省咸阳市高新一中2020-2021学年高一上学期第三次考试数学试题(A卷)云南省丽江市2019-2020学年高一下学期期末数学试题(已下线)考点22 等差数列及其前n项和-备战2022年高考数学(理)一轮复习考点帮贵州省贵阳市清镇北大培文学校2018-2019学年高一下学期期中数学试题(已下线)2020年高考全国3数学文高考真题变式题16-20题吉林省林实验中学2021-2022学年高三上学期开学测试数学(文)试题
名校
解题方法
2 . 已知
为等差数列,前n项和为
,
是首项为2的等比数列,公比大于0,且
,
,
.
(1)求
和
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f42da9081430c4c6b0e48c8bc6274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3408df52e3c9d4b12392a1463bc6ad96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a597f2838a2e6975de78103256c5bc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e66d67b5c93a1f8de640c6935505145.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2875f72cd781842d4b0cb0ac2b526aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a9d3586dcc7fd8bd5e90906b140813.png)
您最近一年使用:0次
2023-03-31更新
|
670次组卷
|
7卷引用:天津市宁河区芦台第一中学2019-2020学年高二上学期第一次月考数学试题
名校
解题方法
3 . 若等差数列的前
项和为
,数列
是等比数列,并且
,
,
,
,
.
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59693a58b316b5b3ef284b4c644a3eba.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/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
您最近一年使用:0次
4 . 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
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/9b08c58baacec3cd0c0a06e267fa9ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4437c6bdb72403891aad57b0fc685d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
5 . 已知等差数列
与正项等比数列
满足
,且
,
,
既是等差数列,又是等比数列.
(1)求数列
和
的通项公式;
(2)①令
,求数列
的前
项和
;
②若对任意的
,不等式
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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a7b35d1812e6745ae7f7c540cf87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c969826f605d65fcf0f7ecf2ff49d4c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)①令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.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)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bef1ed5bfa0e29a7d03f773da37b5a.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
6 . 已知等差数列
的前n项和为
,公差
,且
,
,
,
成等比数列.
(1)求数列
的通项公式;
(2)设
是首项为1,公比为3的等比数列,
(ⅰ)求数列
的前n项和
;
(ⅱ)若不等式
对一切
恒成立,求实数
的最大值.
![](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/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e7b23fd74e3cf89ac541cb7a5d88.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6c852d593cb9f6bdfd9eeddb50fa3.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(ⅱ)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce70396e9a9c2268109b4acb3a23045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-18更新
|
534次组卷
|
3卷引用:天津市滨海新区2023-2024学年高二上学期期末质量检测数学试题
名校
解题方法
7 . 已知等差数列
的前
项和为
,且
.
(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/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/8439fe8fcaea5550194f3245255121a2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ebf05ca12f9da810b2b10e066ececf.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
8 . 已知{
}为等差数列,前n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)求数列
}的前n项和
;
(3)设
,
为数列
的前n项和,求不超过
的最大整数m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c39b984e70553acb2da1012e26ba36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff86be56090d576aad0c0945a6bd2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbaed111f759d66a140168905f2026b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb0344eb6d3543a6c80803e85f60b26.png)
(1)求{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4e296016620fc5dac3fcc871183f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9da2b0e7b9eca965043be2f38a91f1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46784beb9640fb16c3f69ea298404092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526d983bed8be2c14ce68d22e2a74622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d88909e5fcc68bc96d756f2d65060c.png)
您最近一年使用:0次
9 . 已知正项等差数列
与等比数列
满足
,且
既是
和
的等差中项,又是其等比中项.
(1)求数列
和
的通项公式.
(2)求数列
的前
项和
.
(3)设
,记
的前
项和
.若
对于
且
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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd3aff210bb73291e9102bdcc0e6066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea74a5cf39bd1149aed1ce6c8ba0c895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161a7b35d1812e6745ae7f7c540cf87a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015ab2846e43c95c57531067d667066a.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/7c35dd33419fe7539ee8b59deaa84297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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10 . 已知数列
为递增等差数列,数列
为等比数列,且
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292b6a224fc7539b594c8b73d66f8848.png)
(1)求数列
与
的通项公式:
(2)对任意的正整数
,设
,求数列
的前
项和;
(3)求证
.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c1da88d583a3ae4818b9ccc3b1242c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c25a09929ddd94b69868d3048a79a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292b6a224fc7539b594c8b73d66f8848.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230238beeb5b5f30228c16247c63ce24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e9dab25cd410e93bf7de3abb619b11.png)
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