解题方法
1 . 已知数列
满足
,且对任意
均有
.记
的前
项和为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f768d1bbad078c51e76654aac650059f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96791482d4d8b75a49c4e74079aa9d0.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/adf14ebc775db2414a5a960badca8960.png)
A.28 | B.140 | C.256 | D.784 |
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2 . 已知数列
:1,1,2,1,3,5,1,4,7,10,…,其中第1项为1,接下来的2项为1,2,接下来的3项为1,3,5,再接下来的4项为1,4,7,10,依此类推,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
A.![]() |
B.![]() |
C.存在正整数m,使得![]() ![]() ![]() |
D.有且仅有3个不同的正整数![]() ![]() |
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3卷引用:浙江省名校协作体2023-2024学年高二下学期开学适应性考试数学试题
3 . 已知等差数列
的各项均为正数,
.
(1)求数列
的通项公式;
(2)若数列
满足
,求
的通项公式及其前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0503dd6a111356f63a52d4f59ae56fc.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177c4faa4f3fe728621d1478217938ac.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)
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2024-02-27更新
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3卷引用:浙江省七彩阳光联联盟2023-2024学年高三下学期开学考试数学试题
解题方法
4 . 已知数列
,
满足
,
,
,
,
.
(1)求出数列
,
的通项公式.
(2)证明:对任意的
,
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac401d08c490da8fea1593406b286a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f6e3ac00dbca2ef1c99fc041487425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0de859cd92639b9645fb3c0d36b5045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
(1)求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fd6cdb314d3204b17cf5dec0cc8b17.png)
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名校
5 . 已知数列
是等差数列,
是等比数列,且
.则数列![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0554f3270cac65f19edec3cb63e20c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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4卷引用:浙江省“山水联盟”2022-2023学年高三上学期8月返校联考数学试题
浙江省“山水联盟”2022-2023学年高三上学期8月返校联考数学试题黑龙江省大庆市东风中学2022-2023学年高三上学期第一次月考数学试题(已下线)4.3.1 等比数列的概念(精练)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)(已下线)第4讲 等比数列的通项及性质5大题型总结(1)
6 . 已知数列
的各项均为正数,记
为
的前
项和,
(
且
).
(1)求证:数列
是等差数列,并求
的通项公式:
(2)当
时,求证:
.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f9d5d605287823483fef7d09f047ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d1e3a06f59a35396aac6e12c5e2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b55ef1b79628633d81b4a6a70108a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fa69086fde14d466939d2c566a99a2.png)
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6卷引用:浙江省Z20名校联盟(名校新高考研究联盟)2023届高三上学期第一次联考数学试题
名校
解题方法
7 . 已知公差不为零的等差数列{an}和等比数列{bn}满足:
,且
成等比数列.
(1)求数列{an}和{bn}的通项公式;
(2)令
,求数列{cn}的前n项和Sn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8782924aa1a944408ef43334bc27439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93633795bba1868384d1e5b6d8d4894b.png)
(1)求数列{an}和{bn}的通项公式;
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
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10卷引用:浙江省七彩阳光联盟2019-2020学年高一下学期开学考试数学试题
浙江省七彩阳光联盟2019-2020学年高一下学期开学考试数学试题(已下线)2018年高考数学母题题源系列【浙江专版】专题十 等差数列、等比数列及数列的求和【全国百强校】山东省实验中学2015级第二次模拟考试高三数学(理)试题考点10 数列的综合应用-2020年【衔接教材·暑假作业】新高三一轮复习数学(理)(人教版)考点11 数列的综合应用-2020年【衔接教材·暑假作业】新高三一轮复习数学(文)(人教版)福建省泰宁第一中学2019届高三上学期第二阶段考试数学(理)试题陕西省咸阳市武功县2021-2022学年高三上学期第一次质量检测理科数学试题四川省凉山彝族自治州宁南中学2020-2021学年高二下学期第二次月考数学(文)试题河南省周口市扶沟县第二高级中学2021-2022学年高二上学期第一次摸底考试数学试题河南省周口市扶沟县第二高级中学2021-2022学年高二第一次摸底数学试题
8 . 已知数列
的首项
,其前n项和为
,且满足
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,且
,求n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d80fae39643a1ab1ba2c9b8edbc919.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82ecbca314a76a2cc7ba40066813296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23301d258b75999adb64efafd7c8a1c.png)
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浙江省金华市兰溪市第三中学2021-2022学年高二下学期开学考试数学试题江苏省南京市六校2021-2022学年高二上学期期末联考数学试题(已下线)第03讲 等比数列(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)广东省江门市棠下中学2022-2023学年高三上学期数学试题变式题17-22
21-22高二·江苏·假期作业
9 . 已知数列
是等差数列,则下列说法正确的选项有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.数列![]() | B.数列![]() |
C.数列![]() | D.数列![]() |
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3卷引用:浙江省宁波市北仑中学2021-2022学年高二下学期期初考试数学试题
浙江省宁波市北仑中学2021-2022学年高二下学期期初考试数学试题浙江省杭州市富阳区第二中学2021-2022学年高二下学期3月检测数学试题(已下线)第08练 等差数列-2022年【寒假分层作业】高二数学(苏教版2019选择性必修第一册)
名校
解题方法
10 . 已知数列
是公差大于0的等差数列,其前
项和为
,且
成等比数列.
(1)求数列
的通项公式;
(2)设
,其前
项和为
,则是否存在正整数
,使得
成等差数列?若存在,求出
的值;若不存在,请说明理由.
![](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/132c621f42265eb20295b545b8fd89f1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8470f987ac491a2fec4537c7f2d27ba.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/23203e6fe763edf125c6e168a6918587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b162f61b5686e10d09cd750a66cc90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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