1 . 已知数列
,若
,且
.
(1)求证:
是等比数列,并求出数列
的通项公式;
(2)若
,且数列
的前项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998df04d0a8ded946c3f39d545fdc7e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1520ba20cafcdde8521151610fdce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50048f2ab3c89aa1dd2ddb75df35b47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6fb121a57fa35e746f7746d12b67fb4.png)
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2024-01-14更新
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1302次组卷
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4卷引用:陕西省宝鸡市2024届高三上学期高考模拟检测(一)数学(文)试题
解题方法
2 . 已知数列
,若
,且
.
(1)求证:
是等比数列,并求出数列
的通项公式;
(2)若
,且数列
的前n项和为
,不等式
对任意的正整数n恒成立,求实数a的取值范围.
![](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/3998df04d0a8ded946c3f39d545fdc7e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1520ba20cafcdde8521151610fdce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50048f2ab3c89aa1dd2ddb75df35b47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7349518966156f17a35256be6a81db9.png)
您最近一年使用:0次
3 . 已知
为等比数列,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e91dcd541e3ba2ea6311906c3d5cf39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0dfd7836ec0100c7f37688356f5bce.png)
A.216 | B.108 | C.72 | D.36 |
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2024-01-13更新
|
432次组卷
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2卷引用:陕西省部分学校2024届高三下学期二模考试(文科)数学试题
解题方法
4 . 已知等差数列
满足:
,
,其前
项和为
.
(1)求
及
;
(2)若数列
是首项为1,公比为3的等比数列,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338f88d5ad0f6139e3eb4eea16547237.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54786e9cd67005e30a32f61ff97c2a09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
5 . 已知等比数列
的前
项和
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff0a0e9d86aa58e3d139ccb3679460c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.3 | B.9 | C.![]() | D.![]() |
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2024-01-10更新
|
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5卷引用:陕西省商洛市2024届高三上学期尖子生学情诊断考试数学(文科)试题
陕西省商洛市2024届高三上学期尖子生学情诊断考试数学(文科)试题陕西省商洛市2024届高三上学期尖子生学情诊断考试数学(理科)试卷陕西省商洛市2024届高三尖子生学情诊断考试(第二次)数学(理科)试卷(已下线)考点6 等比数列的前n项和的性质 2024届高考数学考点总动员【练】吉林省四平市第一高级中学2023-2024学年高二下学期第一次月考数学试题
解题方法
6 . 已知正项等比数列
中,
成等差数列,其前
项和为
,若
,则
除以7的余数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093bc8d6ed491815d24077d4c72e1740.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/980794e51cc6d0c36de4ce01135099dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
是公差不为零的等差数列,
,且
成等比数列.
(1)求数列
的通项公式;
(2)若
,求
的前1012项和
.
![](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/2a18556fda4a825861f1170cdeb059ff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41ae16f7efb01056246ec77cd471ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee6b547a3be248c012cc94abf603c09.png)
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2024-01-03更新
|
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9卷引用:陕西省西安市西安中学2024届高三模拟考试(九)数学(理科)试题
陕西省西安市西安中学2024届高三模拟考试(九)数学(理科)试题广东省东莞市东华高级中学2024届高三一模数学试题黑龙江省哈尔滨市第三中学2024届高三上学期期末数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)(已下线)考点7 等差、等比数列的联姻 2024届高考数学考点总动员【练】(已下线)专题04 数列(2)(已下线)重难点02:求数列前n项和常用10种解题策略-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)四川省成都市第七中学2024届高三下学期4月分推考试数学(理科)试卷福建省福州第八中学2023-2024学年高二下学期期中考试数学试卷
8 . 已知数列
是公差
不为零的等差数列,其前
项和为
,若
成等比数列,且
.
(1)求数列
的通项公式;
(2)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.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/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52ff4f2d9a76730a7ff5baf43da46f1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ba3491b99cfbbfa5df0433fe8480d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e672c3d231081d12e44a4211e5ac60bf.png)
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2024-01-27更新
|
1231次组卷
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5卷引用:陕西省安康市高新中学2024届高三模拟考试最后一卷理科数学试题
名校
解题方法
9 . 已知数列
的前
项和为
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1483613f3501f6f606b71ce227a3ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
您最近一年使用:0次
10 . 在数列
中,已知
.
(1)求
的通项公式;
(2)求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5156656bf7d5d7da58f2e8e220bec754.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce07afa90e76a49bae2a0e1c0f58414b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-01-10更新
|
1316次组卷
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5卷引用:陕西省安康市高新中学、安康中学高新分校2024届高三上学期第二次“尖子生计划”考试理科数学试题
陕西省安康市高新中学、安康中学高新分校2024届高三上学期第二次“尖子生计划”考试理科数学试题陕西省安康市高新中学、安康中学高新分校2024届高三上学期第二次“尖子生计划”考试文科数学试题河南省周口市项城市2024届高三上学期1月阶段测试数学试题(已下线)模块六 大招1 一阶线性递推(已下线)第2讲:复杂数列通项和求和【练】