名校
解题方法
1 . 公比为
的等比数列
的前
项和
.
(1)求
与
的值;
(2)若
,记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/e6b981758450e9dcee6cfbe6c67c61f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.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/05f5b1a6c081ca11ee5c4723525a43ce.png)
您最近一年使用:0次
2024-01-16更新
|
1321次组卷
|
3卷引用:广东省潮州市2024届高三上学期期末数学试题
名校
解题方法
2 . 已知数列
的前n项和为
,且
.
(1)求证:
是等比数列;
(2)在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,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/72e9b907c54b9b76f3a6d3a9fa56d8ea.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f774872ffec6c34cadeb450cfefdb11e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0526bcbb60d5258b461ab634e913212d.png)
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2023-02-23更新
|
1004次组卷
|
2卷引用:天津市七区2022-2023学年高二上学期期末数学试题
3 . 已知公差不为零的等差数列
的前n项和为
,
,
,
,
成等比数列,数列
的前n项和
.
(1)求数列
和
通项公式;
(2)求
的值;
(3)证明:
.
![](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/36183db0759eec0e108274d229fcd00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d7c4a5263414c45603254e60afe13.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/cd9c5080960098a1799d0eb23e976b3c.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e930426d9c32f1cf4a8ace703fe2dbec.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
的前n项和为
,且
,
.
(1)证明:
为等比数列,并求
的通项公式;
(2)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/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14de5da0d1da50a29fc1e18f860b29ff.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-10-01更新
|
2071次组卷
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9卷引用:吉林省辽源市田家炳高级中学校2022-2023学年高二上学期期末数学试题
吉林省辽源市田家炳高级中学校2022-2023学年高二上学期期末数学试题吉林省辽源市田家炳高中友好学校第七十四届2022-2023学年高二上学期期末联考数学试题河北省示范性高中2023届高三上学期第一次调研数学试题浙江省C8名校协作体2022-2023学年高三上学期第一次联考数学试题四川省隆昌市第七中学2022-2023学年高三上学期11月月考理科数学试题(已下线)4.3 等比数列(3)(已下线)第7讲 数列求和9种常见题型总结 (1)浙江省金华市曙光学校2023-2024学年高二上学期12月月考数学试题(已下线)4.3等比数列(3)
5 . 已知数列
的前
项和为
,满足
,
,
.
(1)证明:数列
是等比数列;
(2)记
,设
,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/b1549723d901eeb2cf966e322f404a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e1a9eec989e8233a81c8149a8991f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6417526489efc14858993d815ad8f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284ecbf2660e975927e51eb68bfc436.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)
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2022-05-13更新
|
1063次组卷
|
3卷引用:辽宁省锦州市2022-2023学年高三上学期期末考试数学试题
名校
解题方法
6 . 已知数列
的前
项和为
,
,
.
(1)证明:数列
为等比数列;
(2)记数列
的前
项和为
,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f3b0ce62abdce77e19fd7ddc9cf1f4.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692a322797d7f1b5a66974b892278238.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.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/9c3fec47d2dd2b8099d86c87b6e57de8.png)
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2022-05-28更新
|
2669次组卷
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9卷引用:湖北省部分县市区省级示范高中温德克英协作体2023-2024学年高二上学期期末综合性调研考试数学试题
湖北省部分县市区省级示范高中温德克英协作体2023-2024学年高二上学期期末综合性调研考试数学试题江苏省南京市教学研究室2022届高三下学期高考前辅导数学试题(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)(已下线)专题19 等比数列及其求和(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)江苏省宿迁市泗洪县洪翔中学2022-2023学年高三上学期暑期学情检测数学试题甘肃省酒泉市玉门油田第一中学2022-2023学年高二上学期10月月考数学试题(已下线)专题05 数列放缩(精讲精练)-1(已下线)专题25 等比数列及其前n项和-1黑龙江省哈尔滨师范大学附属中学2022-2023学年高三上学期期中数学试题
名校
解题方法
7 . 已知数列
的前n项和为
,且
.
(1)证明:数列
是等比数列;
(2)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/add31cf3a48df4a45b0e76cb560b43a3.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-03-03更新
|
631次组卷
|
4卷引用:河南省新乡市2021-2022学年高二上学期期末考试数学(文)试题
河南省新乡市2021-2022学年高二上学期期末考试数学(文)试题河南省新乡市2021-2022学年高二上学期期末考试数学(理)试题湖南省百所学校大联考2021-2022学年高二下学期入学考试数学试题(已下线)湖南省长沙市长郡中学2022届高三下学期月考(六)数学试题
8 . 已知数列
的前
项
.
(1)求数列
的通项公式;
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7c1a9924023ce408b249a32dfd7fe0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd87eb57d157e9a790245eb82d3a5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce6ae3d06eb1ee79e87ef6c86080bca.png)
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2022-03-22更新
|
1297次组卷
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8卷引用:吉林省长春市第二实验中学2022-2023学年高二上学期期末数学试题
9 . 已知数列
中,其前
项和
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f20826a21f6f58bb90915099a84dbe3.png)
.
(1)求证:数列
为等比数列,并求
的通项公式;
(2)设
,求数列
的前项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e22d193eeea7dd2d61f54ea468be716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f20826a21f6f58bb90915099a84dbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866eee57f4f86f03d0d4fc8eb4b8a7f2.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90205cb00b7143a8dcdd2e4cb3f190b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0096ced57c6f31f2e0fe402bd56334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2021-11-26更新
|
594次组卷
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2卷引用:黑龙江省八校2021-2022学年高三上学期期末联合考试数学(理)试题
10 . 已知数列{an}的前n项和为Sn,且Sn=2an
.
(1)证明:数列{an}是等比数列;
(2)设bn=(2n
)an,求数列{bn}的前n项和Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)证明:数列{an}是等比数列;
(2)设bn=(2n
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
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2021-10-04更新
|
652次组卷
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8卷引用:福建省福州市2018届高三上学期期末质检数学(文)试题
福建省福州市2018届高三上学期期末质检数学(文)试题安徽省定远重点中学2019届高三上学期期末考试数学(文)试题【全国百强校】北京师大实验中学2019届高三3月份高考模拟文科数学试题四川省阆中中学2020-2021学年高三上学期开学考试数学(理)试题(已下线)专题04 数列求和(知识串讲)-2020-2021学年高二数学重难点手册(数列篇,人教A版2019选择性必修第二册)(已下线)第19节 数列求和江西省抚州市金溪县第一中学2023届高三上学期第二次月考数学(文)试题四川省成都市玉林中学2023-2024学年高二下学期4月诊断性评价数学试题