已知数列
满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b4d0f4cd51b0889c3abc2004cec58f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b824f17d29a12a52fecbd9440e702bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af242c8a7ae77f1fb73b8038d6c8238e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b4d0f4cd51b0889c3abc2004cec58f.png)
更新时间:2024-02-02 12:41:50
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适中
(0.65)
名校
【推荐1】数列
满足:
,
,①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
_________ ;②若
有一个形如
(
,
,
)的通项公式,则此通项公式可以为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ .(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92876fb436db9b4e97dd42b3e1f713ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fbf186d5f90296e619328e502f75f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89040554aa79926881b74fe954e4d08a.png)
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【推荐2】数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0382b4a2ab0657d2d6830bb6be2b17b6.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e94b7e0d9e764f536997cc0e8e4654e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0382b4a2ab0657d2d6830bb6be2b17b6.png)
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【推荐1】意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样的一列数:
,该数列的特点是: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所组成的数列
称为“斐波那契数列”,则
是斐波那契数列中的第______ 项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a638fcc8e7d8283654e836b24b938d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa371b6d8ee9bd048308878e0b4ea14c.png)
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【推荐2】已知数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7feae546f4d48916ab3a9cac476d5b0.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48c4f8912829cc5ccdc53acb5075527.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d6e2a4dd2bf6f5e1fc8f8414777b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7feae546f4d48916ab3a9cac476d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48c4f8912829cc5ccdc53acb5075527.png)
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解题方法
【推荐1】直线
与直线
相交于点
.直线
与
轴交于点
,过点
作
轴的垂线交直线
于点
,过点
作
轴的垂线交直线
于点
,过点
作
轴的垂线交直线
于点
,
,这样一直作下去,可得到一系列点
、
、
、
,
,点
的横坐标构成数列
.那么,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
_______ 时,
为周期数列;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
_______ 时,
为等比数列.
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516889015009280/2517952847953920/STEM/7de064c292034ad6914444d70d5ccad5.png?resizew=230)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724e81d7db9c33e667abdf6617128b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0e135154ce23f87042c939723e5e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b804d217a03409180af5faf96e98b00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://img.xkw.com/dksih/QBM/2020/7/30/2516889015009280/2517952847953920/STEM/7de064c292034ad6914444d70d5ccad5.png?resizew=230)
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【推荐2】在数列
中,
,
,则
的值为________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0a3ded8440e979f7384753ac69cde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa7daf1bf9c86b7e3eb601281efc5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c28a854eda450ce5a2b68879b11992d.png)
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