2024·全国·模拟预测
解题方法
1 . 已知等比数列
的公比为
,它的前
项积为
,且满足
,
,给出以下命题:①
;②
;③
为
的最大值.其中正确命题的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/50264d5cb22067b076fe3e2376d39f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b4a288ed2eabfaf91963eb54bea320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31add5d92e80dcec34cea2dcec7fd2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5087b65850c79e65452645719f176b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-01-02更新
|
355次组卷
|
5卷引用:4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(八)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(八)(已下线)考点14 数列中的最值问题 2024届高考数学考点总动员(已下线)第1讲:数列的函数性质应用【练】
名校
解题方法
2 . 已知无穷项数列
满足:
为有理数,给出下列四个结论:
①若
,则数列
单调递增;
②数列
可能为等比数列;
③若存在
,则对于任意
,总有
.
④若存在
,对于任意
,总有
,则
.
其中全部正确结论的序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757fa2565058d406171e2c04c81339df.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5faf050789ad292c3c48a72f02fef7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
③若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2144bed075a6332e1c20c7ca81d6ae97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae264151cc27e873d26a7ca105029a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdac33fe562fcb3e15e76be7571d35e.png)
④若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ec09a5b5fd94c1dd994a759907ef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08febc4860b458ef9de6c0d7854dd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
其中全部正确结论的序号为
您最近一年使用:0次
2023-09-04更新
|
443次组卷
|
6卷引用:2023-2024学年高二上学期数学期末预测基础卷(人教A版2019)
(已下线)2023-2024学年高二上学期数学期末预测基础卷(人教A版2019)(已下线)4.3 数列-数列的概念(十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)北京市清华大学附属中学2024届高三上学期开学考试数学试题北京市清华附中2024届高三开学摸底考数学试题北京市广渠门中学2024届高三上学期10月考数学试题北京市第八十中学2023-2024学年高三上学期10月月考数学试卷
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3 . 在数列
中,对任意正整数n都有
,且
,给出下列四个结论:
①对于任意的
,都有
;
②对于任意
,数列
不可能为常数列;
③若
,则数列
为严格增数列;
④若
,则当
时,
.
其中所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56420139e57870e3d5fc9f4057c15f73.png)
①对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c967891f122c574963975c7bc2664fce.png)
②对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40af859d892e1c30f300678e4a05c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492b4cec252b0417cbec8e361718001d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0228078a7a3d05a7643f87e04992a304.png)
其中所有正确结论的序号为( )
A.②④ | B.③④ | C.①②③ | D.②③④ |
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4 . 给出下列四个命题:
①已知直线
,则该直线的倾斜角为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
②抛物线
的准线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
③在等差数列
中,
,若
的前
项和
有最小值,则使
时最大的自然数n的值为2022
④已知数列
,
若对于任意(
)有
,则实数
取值范围是
,
其中正确命题的序号为______ .
①已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698d7ad4f0b131f8287883ed42f79fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
②抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c084abaf8d0b7a5d23f72b51f7cbcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
③在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b0b91048f4a0aed25fe79b82cf299b.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/937228faf3b035ce9fb607ec96f707f0.png)
④已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b68116b0f251eced84cde4aff4bd577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e2f964bb664deba92b0f9ea5f0d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2e3dd29d24da73d27492ac36198889.png)
其中正确命题的序号为
您最近一年使用:0次
解题方法
5 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)当
时,
为递增数列.( )
(2)当
时,
为常数列.( )
(3)
是等比数列,若
,则
.( )
(4)若等比数列
的公比是
,则
(
).( )
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa9bf65189dfb57a61644a1cb27f361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9b26b74b54a192806097b698fac864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d2e59aeab922d37da08fd7c9f517ba.png)
(4)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661f8c3fabb7391571e555c2d325ab81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38b6286e5f74b604b9fb639c55d611f.png)
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6 . 判断正误,正确的写正确,错误的写错误.
(1)1,1,1,1是一个数列.( )
(2)数列1,3,5,7可表示为
.( )
(3)如果一个数列不是递增数列,那么它一定是递减数列.( )
(4)
与
表达不同的含义.( )
(5)数列中的项互换次序后还是原来的数列.( )
(6)所有的数列可分为递增数列和递减数列两类.( )
(7)
与
的意义一样,都表示数列.( )
(1)1,1,1,1是一个数列.
(2)数列1,3,5,7可表示为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602cc5f160a2531da06be7fb0de74f4d.png)
(3)如果一个数列不是递增数列,那么它一定是递减数列.
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(5)数列中的项互换次序后还是原来的数列.
(6)所有的数列可分为递增数列和递减数列两类.
(7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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7 . 已知数列
的通项公式为
,给出下列说法:
①数列
中的最大项和最小项分别是
,
;
②数列
中的最大项和最小项分别是
,
;
③数列
中的最大项和最小项分别是
,
;
④数列
中的最大项和最小项分别是
,
.
其中,说法正确的是_______________ .(填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc17c8b17e65696b26b1fa38a123fe9.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
④数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
其中,说法正确的是
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