1 . 已知数列
满足
,
,且对
,都有
.
(1)设
,证明数列
为等差数列;
(2)求数列
的通项公式.
(3)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3938fc9093a10b040b5ed9d18c876637.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfbfb3bd571b95bdb6a700b443119d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2 . 设公差不为
的等差数列
的首项为
,且
成等比数列.
(1)求数列
的通项公式;
(2)已知数列
为正项数列,且
,设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc54335d4de8adc7c8d5425ba9ee67f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0e24230de5f84e8937dfbd4fb61450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7c561d49be978dafe36601ba26f536.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/8a790ada33239d9fb562525f819a817d.png)
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2024-06-13更新
|
1501次组卷
|
2卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题
3 . 已知数列
满足
,
.
(1)证明数列
是等差数列,并求
的通项公式;
(2)若数列
满足,
,求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e8c3197e04a01871cfdb4d76deb649.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099a64d86bd0b4602578d910322adc1b.png)
![](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/d51fe97bb16c1201ef24e500a846946d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
是数列
的前
项和,
,
是公差为1的等差数列.
(1)求数列
的通项公式;
(2)证明:
.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4419a4be874934e045c20b37a79d13.png)
您最近一年使用:0次
2024-03-25更新
|
2619次组卷
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3卷引用:四川省绵阳市三台中学校2024届高三下学期三诊模拟考试(第三学月月考)文科数学试题
5 . (1)已知
是等差数列
的前n项和,证明:
是等差数列;
(2)已知数列
的通项公式
,前n项和为
,求
取得最小值时n值.
![](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/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d87ed8c93c3821c122b4eeded16bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
解题方法
6 . 在数列
中,
.
(1)证明:数列
为等差数列.
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9287a938e5935cca97c7ab6b42732dbe.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7706e0dba93c9f25c28bc8b01de44b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2024-02-14更新
|
1851次组卷
|
4卷引用:四川省天府新区实外高级中学2023-2024学年高二下学期3月月考数学试卷
四川省天府新区实外高级中学2023-2024学年高二下学期3月月考数学试卷广东省部分学校2023-2024学年高二上学期期末教学质量监测数学试卷广东省中山市迪茵公学2023-2024学年高二下学期开学考试数学试题(已下线)5.3.2 等比数列的前n项和(3知识点+8题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)
名校
解题方法
7 . 等差数列
的前
项和为
,满足
.
(1)求
的通项公式;
(2)设
,求证数列
为等比数列,并求其前
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/1463168eca6f7854ad043366735113d2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c20979da0cb3c6348ee0d3a140a6b13.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)
您最近一年使用:0次
2023-10-08更新
|
1065次组卷
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6卷引用:四川省蓬溪中学校2023-2024学年高三上学期第一次月考理科数学试题
四川省蓬溪中学校2023-2024学年高三上学期第一次月考理科数学试题四川省蓬溪中学校2024届高三上学期第一次月考数学(文科)试题(已下线)模块四 专题6 大题分类练(数列)基础夯实练(人教A)(已下线)第二篇 “搞定”解答题前3个 专题2 数列解答题【讲】 高三逆袭之路突破90分新疆阿勒泰地区2023-2024学年高二上学期期末联考数学试题(已下线)专题09 数列求和6种常见考法归类(1)
8 . 在①
,②其前
项和为
,
③其前
项和为
,
三个条件中任选一个,补充到横线处,并解答.已知数列
为等差数列,
(1)求数列
的通项公式.
(2)若
,证明数列
的前
项和
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0f1e7a333d96ad7f487592dec84bb4.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/99a75943533598609adf0148e37060e9.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/4300dca231e2f4b37f70900b33439d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb742a113460676b91c0d8a72e98b57.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/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
9 . 已知
为等差数列,公差
,且
、
、
成等比数列.
(1)求数列
的通项公式;
(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/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d005409790b3192705a181b2c8e7dfed.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/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
2024-03-08更新
|
2488次组卷
|
6卷引用:四川省大数据学考联盟2024届高三第一次质量检测数学(文科)试题
名校
解题方法
10 . 设等差数列
前
项和
,
,满足
,
.
(1)求数列
的通项公式;
(2)记
,设数列
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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e340d2a0f40f1e823bde5ed026d0c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1122fad4b94aa0836c2d71acc4f315.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546e12c898d812317d8e453f140b9c73.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/5d083a7a5538ad18ca1780f28a183cfe.png)
您最近一年使用:0次
2023-09-21更新
|
1918次组卷
|
7卷引用:四川省绵阳中学2023-2024学年高三上学期一诊模拟(三)数学(理科)试题
四川省绵阳中学2023-2024学年高三上学期一诊模拟(三)数学(理科)试题湖北省黄冈市2023-2024学年高三上学期9月调研考试数学试题(已下线)阶段性检测4.2(中)(范围:高考全部内容)(已下线)第二篇 “搞定”解答题前3个 专题2 数列解答题【练】高三逆袭之路突破90分陕西省兴平市南郊高级中学2024届高三二模数学试题(已下线)专题6.1 等差数列及其前n项和【九大题型】广东省深圳市福田区福田中学2024届高三下学期开学考试数学试题