1 . 已知等差数列{an}的前n项和为Sn,且S5=
S2,a2n=2an+1,n∈N*.
(1)求数列{an}的通项公式;
(2)若
,令cn=an·bn,求数列{cn}的前n项和Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6c4a684e08d7a47b544929c449c054.png)
(1)求数列{an}的通项公式;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f322eed075dac43a3146e6aef41f0c.png)
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6卷引用:天津市咸水沽第一中学2022-2023学年高三上学期线上期末数学试题
天津市咸水沽第一中学2022-2023学年高三上学期线上期末数学试题(已下线)第七章 数列专练9—错位相减求和(大题)-2022届高三数学一轮复习(已下线)专题04数列求和及综合应用之讲案(文科)第一篇 热点、难点突破篇-《2022年高考文科数学二轮复习讲练测》(全国课标版)(已下线)专题04数列求和及综合应用 讲案 (理科)第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测》(全国课标版)安徽省安庆市示范高中2021届高三下学期4月高考模拟理科数学试题新疆伊犁州伊宁市新疆生产建设兵团第四师第一中学2024届高三下学期3月月考数学试题
名校
2 . 在递增的等差数列
中,
,
,则公差
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bbf91a7f4fd336fc777c0c65bf66bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f7afa7c2e0ddcc1dd303416edd106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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5卷引用:天津市武清区杨村第一中学2022-2023学年高三上学期第一次月考数学试题
名校
解题方法
3 . 已知等差数列
和
的前
项和分别为
和
,且有
,
,则
的值为( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b53ad0035d00374e2e2f895edc6153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86d287400cafbacdbe3054b86a91b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dba965472ad9713730902e808d84273.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:天津经济技术开发区第一中学2023届高三上学期期中数学试题
天津经济技术开发区第一中学2023届高三上学期期中数学试题(已下线)专题8 数列河南省豫西名校2021-2022学年高二上学期第一次联考数学试题河南省实验中学2021-2022学年高二上学期期中数学(文)试题(已下线)第03讲 等差数列的前n项和公式-【帮课堂】2021-2022学年高二数学同步精品讲义(人教A版2019选择性必修第二册)
名校
解题方法
4 . 已知数列
的前
项和为
,数列
满足
,
,
.
(1)求数列
,
的通项公式;
(2)若
,数列
的前
项和为
,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/a027e8759ec0f9d311e49d8215169c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c696fb6d4ba3550fe987bb45f7fff447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(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/d2dfb79027a580ee2f328bc83d86ce09.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/9456bdf03b6f4eb7679049f8473923dc.png)
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5卷引用:天津市第一中学2022届高三下学期统练6数学试题
天津市第一中学2022届高三下学期统练6数学试题天津市耀华中学2022届高三下学期高考前冲刺(二)数学试题(已下线)专题24 数列求和的常见方法-学会解题之高三数学万能解题模板【2022版】浙江省百校2021-2022学年高三上学期开学联考数学试题第四章数列单元检测卷(B卷综合篇)-2021-2022学年高二数学同步单元AB卷 (人教A版2019选择性必修第一册+第二册,浙江专用)
5 . 已知等差数列
中,
,
,数列
满足
,
.
(1)求
,
的通项公式;
(2)记
为数列
的前
项和,试比较
与
的大小;
(3)任意
,
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d77060931748cee8c21b43d15033b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb85bc5382536c69e33043b1903f9bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d513d1290bfc8265f7a1a1ea99cc8fc.png)
(1)求
![](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/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/767e50e27e24712d5ec33e2130212941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22d144b564ca92fae36a5f454952553.png)
(3)任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78abdd4d4340e8f1a869f9a3f41729a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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5卷引用:天津市西青区杨柳青第一中学2022届高三下学期第六次适应性测试数学试题
天津市西青区杨柳青第一中学2022届高三下学期第六次适应性测试数学试题天津市第一中学2021-2022学年高三上学期第二次月考数学试题天津市第二中学2021-2022学年高三上学期统练(二)数学试题四川省成都市新都区2020-2021学年高一下学期期末数学试题(已下线)专题03 《数列》中的压轴题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
6 . 已知等比数列
的前n项和为
,公比
,
,
,数列
满足
且
,
.
(1)求
和
的通项公式;
(2)将
和
中的所有项按从小到大的顺序排列组成新数列
,求数列
的前
项和
;
(3)设数列
的通项公式为:
,
,求
.
![](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/f71acdb04454c77e1e25ad4f336cccfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4c2d452851c386cdedf3261d9e9053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a3a7fd0728cef9ad17e2081949f7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83432083c2c8649c9247e3d17986e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e78f07af568e395269122824300b039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559304a6650e8c5043d0e9efbdcf8cfa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)将
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00136ab4fd69ba9c28b47cd38442dc3a.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bdb3b92120f5a996b660971ce60be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecc554fa88de158f1932b874c90765d.png)
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天津市第四十七中学2022届高三下学期学业能力调研数学试题天津市滨海新区塘沽第一中学2022届高三下学期4月线上统练数学试题天津市武清区杨村第一中学2021届高三下学期高考热身训练一数学试题天津市滨海新区塘沽第一中学2020-2021学年高三上学期第二次月考数学试题(已下线)专题09 数列求和(奇偶项讨论)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)
7 . 已知
为等差数列,
为等比数列,
,
,
.
(1)分别求数列
和
的通项公式;
(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,
(i)求证
;
(ii)对任意的正整数
,设
,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/38795ba10dc132a5c881c55662c59481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20d20643cd69ac1cac8b61be63a58da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45719bf94d0e81e237fa90d097032445.png)
(1)分别求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(i)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f14c8d93ae394a608ccdf7f1a370.png)
(ii)对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c601b88d9c5fd4ec4e2e82e2c417e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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6卷引用:天津市第一中学滨海学校2022届高三下学期第一次质量调查数学试题
天津市第一中学滨海学校2022届高三下学期第一次质量调查数学试题天津市新华中学2021届高三下学期第八次统练数学试题(已下线)数学-2022年高考押题预测卷02(江苏专用)(已下线)信息必刷卷03(天津专用)(已下线)一轮复习大题专练40—数列(讨论奇、偶2)-2022届高三数学一轮复习(已下线)专题09 数列求和(奇偶项讨论)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)
8 . 设数列
为等差数列,其前
项和为
,数列
为等比数列.已知
,
,
.
(1)求数列
和
的通项公式;
(2)求数列
的前
项和;
(3)若
,
,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/04e406b775bbaa0ae52dab5b7bd384a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc27067aeecc07fc725ce30d3021636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2e6956e0073cef684fef6a16bead0a.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/b52c9237cb0b4acc568d4afb12997186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71252376ee7ac17ac09f143f853b614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4卷引用:天津市滨海新区塘沽第十三中学2022-2023学年高三上学期第一次月考数学试题
天津市滨海新区塘沽第十三中学2022-2023学年高三上学期第一次月考数学试题天津市朱唐庄中学2022-2023学年高三上学期期末数学试题天津市河北区2021届高三下学期总复习质量检测(二)数学试题(已下线)第七章 数列专练8—裂项相消求和(大题)-2022届高三数学一轮复习
9 . 设
是等差数列,
是等比数列,公比大于0,其前
项和为
.已知
,
,
,
.
(Ⅰ)求
和
的通项公式;
(Ⅱ)设数列
的前
项和
.记
,求
;
(Ⅲ)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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9e0490a0d021ff5eb6bddd42e02307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed438eb9a5489371009ffe76a055c86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b696992c08553751ccbc7e43ac5e1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df586adaf9eb4b97ac26fbfe966629bc.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f20326e3bf65ccb3669cd226dfb73d6.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/e5deb6f3cec6b368c21e4e8e41b02fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(Ⅲ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf02c3987690dbd6cbc457d101fa4f.png)
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4卷引用:天津市红桥区2022届高三下学期二模数学试题
天津市红桥区2022届高三下学期二模数学试题天津市南开区2021届高三下学期二模数学试题(已下线)第七章 数列专练9—错位相减求和(大题)-2022届高三数学一轮复习天津市南开中学2021-2022学年高三上学期第四次学情调查数学试题
10 . 已知等比数列
是递减数列,
的前
项和为
,且
成等差数列,
.数列
的前
项和为
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a31a71ee08c2cb22f89710d37a92d9d.png)
(1)求
和
的通项公式:
(2)若
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1e4048372d28b0170755dc86489e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc8149091bd8d714b2575053bf1ae50.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/6a31a71ee08c2cb22f89710d37a92d9d.png)
(1)求
![](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/dcc4cfcd6766074146bb7597f05ce114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68607170e4fa90d4eb91848036839e0c.png)
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5卷引用:天津市河东区2022-2023学年高三上学期期末数学试题
天津市河东区2022-2023学年高三上学期期末数学试题天津市和平区2021届高三下学期第二次质量调查数学试题(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天津市第二南开学校2022-2023学年高三下学期开学学情调查数学试题山西大学附属中学校2022-2023学年高二下学期3月月考数学试题