名校
解题方法
1 . 设数列
的前n项和为
,满足
.
(1)求数列
的通项公式
;
(2)记
,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/c8370a173854471a3eb27637993a3d5d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c58fd95a0f3d0c5e0bd3e6b28deb969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7c561d49be978dafe36601ba26f536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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5卷引用:四川省南充市西充中学2023-2024学年高二下学期期中考试数学试题
解题方法
2 . 已知
是公差为d的等差数列,其前n项和是
,且
,
.
(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/cd807f60189a561ac93ed025445c787e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7037f2d5fb7799e24df151ac5d6ad6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2卷引用:安徽省滁州市定远县育才学校2021-2022学年高二分层班下学期期中考试数学(理)试题
3 . 数列
的前
项和为
,
,
.
(1)求数列
的通项公式;
(2)记数列
,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/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3715b885f66a3ea6dd527975a90af0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2366d8d61a81a296a898fc50d8db6d75.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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3卷引用:江西省南昌市第十九中学2022-2023学年高二下学期期中考试数学试卷
4 . 数列
满足
,则数列
的前n项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ce10bdd0a393af4aa464060fb19f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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17卷引用:【全国百强校】北京101中学2018-2019学年下学期高一年级期中考试数学试卷
【全国百强校】北京101中学2018-2019学年下学期高一年级期中考试数学试卷天津市和平区耀华中学2019-2020学年高二上学期期中数学试题(已下线)2019年9月23日 《每日一题》2020年高考理数一轮复习-数列的通项与求和(1)(已下线)2019年9月25日 《每日一题》2020年高考文数一轮复习-数列的通项与求和(1)安徽省蚌埠第二中学2019-2020学年高二上学期8月暑期测试数学试题(已下线)2.5+等比数列的前n项和(2)(基础练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版必修5)人教A版(2019) 选择性必修第二册 过关斩将 第四章 数列 4.2 等差数列 4.2.2 等差数列的前n项和公式 第1课时 等差数列前n项和及其性质基础过关练(已下线)考点13+数列的应用-2020-2021学年【补习教材·寒假作业】高二数学(人教B版2019)(已下线)4.3.2 等比数列的前n项和(2)(基础练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版选择性必修第二册)天津市耀华中学2020-2021学年高二上学期期末数学试题北京东城东直门中学2021-2022学年高二9月月考数学试题安徽省芜湖市2021-2022学年高二上学期期末数学试题四川省遂宁市射洪中学校2022届高三下学期高考适应性考试数学(文科)试题天津市天津中学2022-2023学年高二上学期期末数学试题(已下线)2019年12月29日《每日一题》必修5+选修2-1理数-每周一测天津市复兴中学2021-2022学年高三上学期第一次月考数学试题广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题
5 . 已知数列
的首项
,且满足
.
(1)证明:数列
为等比数列,并求出数列
的通项公式;
(2)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/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4b89957e7481310c34f93ff81d43cb.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0946b13cc360976aea85a222f66cc7f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c02123d36cb17d6a30357fd0457824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19a6a8737d38c958d1443a7414e237f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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4卷引用:河南省濮阳市第一高级中学2021-2022学年高二下学期期中考试数学(文)试题
名校
解题方法
6 . 已知数列
的前n项和为
,且
,则数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](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/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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5卷引用:广东省深圳中学2022-2023学年高二上学期期中数学试题
名校
解题方法
7 . 已知
和
分别是数列
和
的前
项和,且满足
,
,若对
,使得
成立,则实数
的取值范围是( )
![](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/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/5d684b92cccda797a5fb4bddb0eb2aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c128315a1b3539cb1b0ad246fb2dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5636df800895cdef383fbbe65e1c18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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6卷引用:陕西省咸阳中学2022-2023学年高二上学期期中理科数学试题
陕西省咸阳中学2022-2023学年高二上学期期中理科数学试题河北省唐山市2021-2022学年高二上学期期末数学试题河北省唐山市2022-2023学年高二上学期期末模拟数学试题(已下线)4.3.2 等比数列的前n项和公式(2)广东省深圳市深圳外国语学校2024届高三上学期第二次模拟测试数学试题(已下线)广东省深圳市深圳外国语学校2024届高三上学期第二次模拟测试数学试题变式题1-5
2022高三·全国·专题练习
8 . 数列
满足
,
.
(1)求
,
,
的值;
(2)求数列
的通项公式;
(3)设
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85a128d86aae4c8b0b6ea56e9335bea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b3193369d1b54f37855ba7c3a7216b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-01-13更新
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3卷引用:江西省全南中学2022-2023学年高二下学期期中数学试题
9 . 已知数列
的前
项和为
,在①
②
,③
这三个条件中任选一个,解答下列问题.
(1)求出数列
的通项公式;
(2)若设
,数列
的前
项和为
,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
注:如果选择多个条件分别解答,按第一个解答计分.
![](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/2edeb1f47dfcc97e3317bd3b66c84517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d3ad744c3967aa85dead18e9d17cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610bf0995865773e408651b22c229033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af86bc4de5ef8fb1c97ca66ef4720a65.png)
(1)求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7484eb1c64c64773677976d8e6281af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.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/f9928e46511e601913619a427ded84a3.png)
注:如果选择多个条件分别解答,按第一个解答计分.
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5卷引用:广东省广州科学城中学2021-2022学年高二下学期期中数学试题
10 . 在数列
中,
.
(1)求
的通项公式.
(2)设
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cd83e7c9a890dd4c9db48ef4f4ce6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](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/b18cddc166710033aba45b4e98329fce.png)
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