2024·全国·模拟预测
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1 . 记递增的等差数列
的前
项和为
.若
,则
( )
![](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/be9e8bb7cde788a6059cd9ee9a60531b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
A.![]() | B.125 | C.155 | D.185 |
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2024-01-14更新
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712次组卷
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3卷引用:江苏省姜堰中学2024届高三下学期阶段性测试(2.5模)数学试题
2 . 在①
成等比数列,②
,③
这三个条件中任选两个,补充在下面问题中,并完成解答.
已知数列
是公差不为0的等差数列,其前
项和为
,且满足__________,__________.
(1)求
的通项公式;
(2)求
.
注:如果选择多个方案分别解答,按第一个方案计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8aa010f7105f3ca426c8a34880abd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097f7e688074baee9d9a8e7b1468808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0954b93b4429f74f75da36dab440226.png)
已知数列
![](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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b47d8120f7f1344d58d3ddf37a9eb47.png)
注:如果选择多个方案分别解答,按第一个方案计分.
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7卷引用:江苏省泰州市2023届高三下学期第一次调研测试数学试题
3 . 记数列
的前n项之积为
.
(1)若
为等比数列,
,
,求
;
(2)若
为等比数列,
,
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939366f52d33ae3f69b101251eaa02da.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b4e688ad5156121531f6e0f4b4c1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68e340c43602bb6d26a74a1fbd2dea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b4e688ad5156121531f6e0f4b4c1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68e340c43602bb6d26a74a1fbd2dea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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3卷引用:江苏省泰州市2021届高三下学期考前练笔数学试题
江苏省泰州市2021届高三下学期考前练笔数学试题广东省中山市2021-2022学年高二上学期期末数学试题(已下线)4.3.1 等比数列的概念(第1课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)
4 . 已知等差数列
的前
项和为
,公差为整数,现有四个等式:①
;②
;③
;④
,若其中有且只有一个等式不成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627411fce8e2b6ab40ac1166b45ada6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5170584604571b5e1afd5ece941e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
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2021-06-04更新
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6卷引用:江苏省泰州市2021届高三下学期考前练笔数学试题
江苏省泰州市2021届高三下学期考前练笔数学试题(已下线)专题09 等差数列-2022年高考数学一轮复习小题多维练(新高考版)沪教版(2020) 25天高考冲刺 双新双基百分百20(已下线)【新教材精创】 5.2.2 等差数列的前n项和 -A基础练(已下线)4.2等差数列(B 能力培优练)-2021-2022学年高二数学同步双培优检测(苏教版2019选择性必修第一册)(已下线)第四章 数列单元测试-2021-2022学年高二数学同步精品课堂讲+例+测(苏教版2019选择性必修第一册)
5 . 已知
为等差数列,
分别是下表第一、二、三行中的某一个数,且
中的任何两个数都不在下表的同一列.
请从①
,②
,③
的三个条件中选一个填入上表,使满足以上条件的数列
存在;并在此存在的数列
中,试解答下列两个问题.
(1)求数列
的通项公式;
(2)设数列
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/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
第一列 | 第二列 | 第三列 | |
第一行 | |||
第二行 | 4 | 6 | 9 |
第三行 | 12 | 8 | 7 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca0fafd37a2d8667fa499dd35d7414f.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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11卷引用:江苏省泰州中学2021届高三下学期四模数学试题
江苏省泰州中学2021届高三下学期四模数学试题山东省青岛市2020届高三第三次模拟数学试题山东省青岛市2020届高三自主检测数学试卷(已下线)专题四 数列-山东省2020二模汇编(已下线)新高考题型:开放性问题《数列》湖南省长沙市雅礼中学2020-2021学年高三上学期月考(三)数学试题广东省深圳市盐田区深圳外国语学校2021届高三上学期1月月考数学试题广东省广州市执信中学2021届高三上学期第四次月考数学试题(已下线)第30讲 数列的综合应用(练)- 2022年高考数学一轮复习讲练测(课标全国版)(已下线)专题05 策略开放型【练】【通用版】江苏省无锡市天一中学2020-2021学年高二下学期期末学情检测数学试题
6 . 已知正项等差数列
的前
项和为
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.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/8627fb57f6ce8383d3f1118ff368204d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fce21bf93e1492b6d657a851d189e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
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名校
7 . 等差数列
的公差为2,
是数列
的前n项的和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6438f0e898418b170203743a44e2499b.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](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/bf6be64aa7306cfb8504ad1e31d26cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6438f0e898418b170203743a44e2499b.png)
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名校
解题方法
8 . 设
为等差数列
的前
项和,若
,
,则
的值为__________ .
![](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/6bf8830d5ac299a7f9165552a0c5d01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23cce98137e86b3467d9d3a0c595538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
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2卷引用:江苏省泰州市泰兴市黄桥中学2020届高三下学期高考模拟数学试题
名校
9 . 设
为等差数列
的前
项和,若
,
,则
的值为_____ .
![](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/afbd2b6ea3669d46643be552e7ea3904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b0d308e80c1d3fbb751c050ce4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
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4卷引用:【校级联考】江苏省泰州中学等2019届高三第二学期联合调研测试数学试题
【校级联考】江苏省泰州中学等2019届高三第二学期联合调研测试数学试题江苏省泰州中学、宜兴中学等校2019届高三4月联考数学试题(含附加题)【校级联考】江苏省高三泰州中学、宜兴中学、梁丰2019届高三第二学期联合调研测试数学试题(已下线)专题6.2 等差数列及其前n项和(练)-江苏版《2020年高考一轮复习讲练测》