名校
解题方法
1 . 已知数列
是公差为2的等差数列.
(1)若
成等比数列,求
的值;
(2)设
,数列
的前n项和为
.数列
满足
.记
,求数列
的最小项
(即
对任意
成立).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920ad6b9e7f1c2c4a5a3025ba57e71b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff6bd0b129ecb5c0ecfb3190a269ad0.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9358ef249b920a98e761184e2cba45a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9fb36a51456d5f5f061a3c10c3ccff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db844dc31684da771e0a5dc2f5ece11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f203d39a87ac7a57a097abac7d6b5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
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2021-03-26更新
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2卷引用:2016年上海市普通高中学业水平考试数学试题
解题方法
2 . 数列
满足
,若
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a79b11c6a81e52c9245ac74a800375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0001a5d4a96049e247b7bd49a5986e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 若等差数列
满足
,则
的前7项的和为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0abedd59476f8793d5a8948590a70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e6b4ede9113dcff778da5ac6138c4d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e6b4ede9113dcff778da5ac6138c4d.png)
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2021-01-18更新
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82次组卷
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2卷引用:2017 年上海市普通高中学业水平合格性考试数学试题
5 . 无穷等比数列
的首项为
,公比为
,则
的各项的和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2019-12-17更新
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2卷引用:2016年上海市普通高中学业水平考试数学试题
6 . 若首项为2的无穷等比数列
的各项的和为10,则公比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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2019-11-08更新
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2卷引用:2017 年上海市普通高中学业水平合格性考试数学试题
名校
7 . 给定无穷数列
,若无穷数列
满足:对任意
,都有
,则称
与
“接近”.
(1)设
是首项为
,公比为
的等比数列,
,判断数列
是否
与
接近,并说明理由;
(2)设数列
的前四项为:
,
,
,
,
是一个与
接近的数列,记集合
,求
中元素的个数
;
(3)已知
是公差为
的等差数列,若存在数列
满足:
与
接近,且在
,
,…,
中至少有
个为正数,求
的取值范围.
![](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/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dd644fc0373b59f11179da6a242bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)设
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2c0bdead124cca6b0083509f8eb3ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1038200f2d97a52c716aab6c3bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c5c4ac959eb2c4b74afabc9cdd3a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6085ef7d087cdf7c117978dcfce3f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aec1e4ca31a14444f4bc8682ab5d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a37c2996e097b38235498876dadbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffdba64d0b29ba1f87bba807c82395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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2018-09-20更新
|
2217次组卷
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8卷引用:2018年全国普通高等学校招生统一考试数学(上海卷)
2018年全国普通高等学校招生统一考试数学(上海卷)上海市七宝中学2018-2019学年高二上学期9月摸底数学试题北京市第八中学2020-2021学年高二下学期期中数学试题北京八一学校2022届高三上学期开学考试数学试题(已下线)专题09 数列-五年(2017-2021)高考数学真题分项(新高考地区专用)(已下线)专题16 数列新定义题的解法 微点2 数列新定义题的解法(二)(已下线)专题21 数列解答题(理科)-2(已下线)专题21 数列解答题(文科)-2
8 . 设等比数列
的通项公式为
,前
项和为
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce137adfad68296c3fc95a2ef62b0d7.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/322d626bd99319159a24b2b21aa1782a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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3卷引用:2018年全国普通高等学校招生统一考试数学(上海卷)
2018年全国普通高等学校招生统一考试数学(上海卷)上海市嘉定区封浜高级中学2019-2020学年高二上学期期中数学试题(已下线)专题09 数列-五年(2017-2021)高考数学真题分项(新高考地区专用)
名校
9 . 记等差数列
的前
项和为
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf14ebc775db2414a5a960badca8960.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/58365ff21052f2f978c11844b002b933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3aaa752e654842dfe0e705b9626b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf14ebc775db2414a5a960badca8960.png)
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5825次组卷
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13卷引用:2018年全国普通高等学校招生统一考试数学(上海卷)
2018年全国普通高等学校招生统一考试数学(上海卷)上海市宜川中学2018-2019学年高三上学期12月月考数学试题上海嘉定区安亭高级中学2019-2020学年高二上学期第一次月考数学试题上海市行知中学2021届高三上学期开学考试数学试题上海市进才中学2023届高三下学期3月月考数学试题江苏省南京市江宁区2018-2019学年高二第二学期期末学情调研卷数学试题(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项(已下线)第22练 等差数列-2021年高考数学(理)一轮复习小题必刷(已下线)第21练 等差数列-2021年高考数学(文)一轮复习小题必刷(已下线)专题09 数列-五年(2017-2021)高考数学真题分项(新高考地区专用)(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)(已下线)专题22 等差等比数列性质的巧用-学会解题之高三数学万能解题模板【2022版】(已下线)考向19等差数列及其前n项和(重点)-3
2012高三上·上海·学业考试
10 . 设等比数列
的前
项和为
,已知
.
(1)求数列
的通项公式;
(2)在
与
之间插入
个1,构成如下的新数列:
,求这个数列的前
项的和;
(3)在
与
之间插入
个数,使这
个数组成公差为
的等差数列(如:在
与
之间插入1个数构成第一个等差数列,其公差为
;在
与
之间插入2个数构成第二个等差数列,其公差为
,…以此类推),设第
个等差数列的和是
. 是否存在一个关于
的多项式
,使得
对任意
恒成立?若存在,求出这个多项式;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/0ed89594f82c84675634a76c572d0cd3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32091a4547697333528bcb51b621fcec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856596a200703d8db67e5d920752591a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9824e0c876f4122f0c5952de29e5a1.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.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/5edf900c810371fb21297c15f86d8743.png)
![](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/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d29c5183c30d5ce10d42b475c4f815f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
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