名校
解题方法
1 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环圈
.这就是数学史上著名的“冰雹猜想”(又称“角谷猜想”).如取正整数
,根据上述运算法则得出
,共需经过8个步骤变成1(简称为8步“雹程”).现给出冰雹猜想的递推关系如下:已知数列
满足:
(
为正整数),
当
时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3967d620e2fef3ecc724c66e29f68a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73700b5135fc6a9c2d923a27a4c9b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4914df4e75585d5ff7709d64a23611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59097ad7c8f3fcff871ad48933d30498.png)
A.170 | B.168 | C.130 | D.172 |
您最近一年使用:0次
2024-01-12更新
|
922次组卷
|
4卷引用:信息必刷卷04(天津专用)
2 . 已知数列
的各项是奇数,且
是正整数
的最大奇因数,
.
(1)求
的值;
(2)求
的值;
(3)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97daaae5be89c76c7ccb25fd96339b46.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab24d03d347b53c928e704601e68a7d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
您最近一年使用:0次
2024-05-08更新
|
1018次组卷
|
3卷引用:5.2 等差数列和等比数列(高考真题素材之十年高考)
3 . 若数列
满足
,
,则称该数列为斐波那契数列.如图所示的“黄金螺旋线”是根据斐波那契数列画出来的曲线.图中的长方形由以斐波那契数为边长的正方形拼接而成,在每个正方形中作圆心角为
的扇形,连接起来的曲线就是“黄金螺旋线”.记以
为边长的正方形中的扇形面积为
,数列
的前n项和为
.给出下列结论:
;
②
是奇数;
③
;
④
.
则所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be7f38256b38b88ac5c7d5cec9d407d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0578e8a21d22742c35bd1c32f7d06f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88126c3cbc88e03d38f56b7da315b6.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f91a9239ff99733ea1b9128aa47bb96.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624c34f6817447eec429659e52ad178e.png)
则所有正确结论的序号是
您最近一年使用:0次
2023-08-05更新
|
855次组卷
|
4卷引用:【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编
【北京专用】专题03数列(第三部分)-高二上学期名校期末好题汇编(已下线)专题02 等比数列4种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北京专用)(已下线)4.3.2 等比数列的前n项和公式——课后作业(提升版)北京市房山区2022-2023学年高二下学期期末数学试题
4 . 已知
是公比为q的等比数列.对于给定的
,设
是首项为
,公差为
的等差数列
,记
的第i项为
.若
,且
.
(1)求
的通项公式;
(2)求
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecea6aa3b0b367dbd8d0e38c65829c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac24dd2ff15d115696e8a9f8dad264f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c66a0c50c32fba396a322f0ddbeda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac24dd2ff15d115696e8a9f8dad264f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f686d89f95d2dc846e53eab5ca99ddde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33c0acaa66514a4f1493b158ebd09e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2608df648efc5364a2dc2c67cfe14cd9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27dd9877202542cc6975d5a4d78724a.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88b0922dc08ae6398dfc0296037c759.png)
您最近一年使用:0次
2023-05-20更新
|
1166次组卷
|
3卷引用:第05讲 数列求和(练习)
5 . 若有穷自然数数列
:
满足如下两个性质,则称
为
数列:
①
,其中,
表示
,这
个数中最大的数;
②
,其中,
表示
,这
个数中最小的数.
(1)判断
:2,4,6,7,10是否为
数列,说明理由;
(2)若
:
是
数列,且
,
,
成等比数列,求
;
(3)证明:对任意
数列
:
,存在实数
,使得
.(
表示不超过
的最大整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5fe1c847904911c89504cef0973214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1445aef0f66cacf3c0b358775623fab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94beabf4bfbaa67081f1755fa5553a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598a5ba40123abea0f6e4559535a61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daaf260a47403a2bdddd1268ebc44cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a878ab2590307a7a6f7afe576b7112c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1cb4ffc937e336200fd70fc089041a.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e005b9c19a9b287aeefaa3af850beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
6 . 已知数列
满足:对任意的
,总存在
,使得
,则称
为“回旋数列”.以下结论中正确的个数是( )
①若
,则
为“回旋数列”;
②设
为等比数列,且公比q为有理数,则
为“回旋数列”;
③设
为等差数列,当
,
时,若
为“回旋数列”,则
;
④若
为“回旋数列”,则对任意
,总存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8494594299d0ecce6e1e52151f402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3693c7c942afef5517a3c18997c878df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542ed562aec60ccb50d3b7a478dff2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
③设
![](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/d2d8bbb4a09e0ac86bbae46222a90841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60acf58bad78854a0db851c42f739543.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8494594299d0ecce6e1e52151f402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de197a4e711c2f391eca67ad8807e088.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2023-05-26更新
|
992次组卷
|
7卷引用:专题02 结论探索型【练】【北京版】
(已下线)专题02 结论探索型【练】【北京版】(已下线)黄金卷06(已下线)重难点突破01 数列的综合应用 (十三大题型)-1北京市人大附中2023届高三三模数学试题上海市延安中学2024届高三上学期开学考数学试题上海市延安中学2024届高三上学期9月月考数学试题上海市鲁迅中学2024届高三上学期期中数学试题
名校
解题方法
7 . 在一个数列中,如果每一项与它的后一项的和为同一个常数,那么这个数列称为等和数列,这个常数称为该数列的公和.已知数列
是等和数列,且
,
,则这个数列的前2022项的和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2815b24f5a89be7ae53aed93182e8988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d542d4679d36cc6f9f6a1d5aced714e.png)
您最近一年使用:0次
2023-03-02更新
|
954次组卷
|
6卷引用:第05讲 数列求和(练习)
(已下线)第05讲 数列求和(练习)(已下线)专题03等差数列与等比数列(已下线)专题10 押全国卷(文科)第10、13题 数列(已下线)专题12 等和数列 微点2 等和数列综合训练安徽省淮北师范大学附属实验中学2022-2023学年高二下学期第一次月考数学试题甘肃省兰州市第五十八中学2022-2023学年高三下学期第二次模拟考试数学(理科)试卷
名校
8 . 在数列
中,
(
为非零常数),则称
为“等方差数列”,
称为“公方差”,下列对“等方差数列”的判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44818d415cf4e4af51151193e204bdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e66570190766ac3f932bcfae98cadc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.![]() |
B.若正项等方差数列![]() ![]() ![]() ![]() |
C.等比数列不可能为等方差数列 |
D.存在数列![]() |
您最近一年使用:0次
2023-08-04更新
|
909次组卷
|
5卷引用:模型1 用综合法快解新情境背景下的数列创新题模型(高中数学模型大归纳)
(已下线)模型1 用综合法快解新情境背景下的数列创新题模型(高中数学模型大归纳)(已下线)微专题1 数列综合应用-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)云南省三校2024届高三高考备考实用性联考卷(一)数学试题福建省宁德第一中学2023-2024学年高二上学期开学检测数学试题广东省佛山市第一中学2024届高三上学期12月月考数学试题
名校
9 . 意大利著名数学家斐波那契在研究兔子的繁殖问题时,发现有这样的一列数:1,1,2,3,5,8,13,21,….该数列的特点如下:前两个数均为1,从第三个数起,每一个数都等于它前面两个数的和.人们把这样的一列数组成的数列
称为斐波那契数列,现将
中的各项除以2所得的余数按原来的顺序构成的数列记为
,数列
的前n项和为
,数列
的前n项和为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.![]() |
您最近一年使用:0次
2023-05-23更新
|
979次组卷
|
12卷引用:【一题多变】斐波那契数列1
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名校
10 . 对于数列
,若存在正数
,使得对一切正整数
,恒有
,则称数列
有界;若这样的正数
不存在,则称数列
无界,已知数列
满足:
,
,记数列
的前
项和为
,数列
的前
项和为
,则下列结论正确的是( )
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A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
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2022-03-24更新
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