2023高三·全国·专题练习
1 . 已知数列
满足:
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3195293a26b9bf357e2be8a1bc30f514.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115da54f93de5e89d1e7f443fccb61f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689dd8567069094ef56a1aa7be3f6184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3195293a26b9bf357e2be8a1bc30f514.png)
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2 . 对于数列
,如果存在最小的一个常数
,使得对任意的正整数恒有
成立,则称数列
是周期为
的周期数列.设
,数列前
项的和分别记为
,则
三者的关系式_____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227ab551cad3c1297402f29fc9d32435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2b94cbf8f1acc77ed2618d9ba5756a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207912f4831483319d42adfd9bc40d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d04c40711df685486acacfff234fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d917c6c2bc767e1e63b90854c231a290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d917c6c2bc767e1e63b90854c231a290.png)
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2023高三·全国·专题练习
解题方法
3 . 把下面不完整的命题补充完整,并使之成为真命题.
已知数列
满足
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
______ ,则数列
的前2023项积为______ .
注:填上你认为可以成为真命题的一种情形即可.
已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
注:填上你认为可以成为真命题的一种情形即可.
您最近一年使用:0次
2023·上海浦东新·模拟预测
名校
4 . 已知
,且
(
为正整数),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cefeddf71dca8ae824328df3f0e5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3172a2dfbce3ce32fd909ff548e75b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
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2023高三·全国·专题练习
5 . 在数列
中,已知
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.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/cd5359c8fdc022d7044ffb6fdb291666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a385625030dd39a66e1e12324b71e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
您最近一年使用:0次
2023高三·全国·专题练习
6 . 已知数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f70f7d6f42fc6f7b662d69bc5c1d6b4.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbadb0fb97c4913ff3687415596348d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46c2b59c48b8680c8b3e206d92ef074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f70f7d6f42fc6f7b662d69bc5c1d6b4.png)
您最近一年使用:0次
2023高三·全国·专题练习
7 . 已知数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
您最近一年使用:0次
2023高三·全国·专题练习
8 . 在数列
中,已知
,
,则
的前100项的和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.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/cf074f13d5ddc6301eda00e07058e87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
您最近一年使用:0次
2023高三·全国·专题练习
9 . 在数列
中,已知
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2f03f58e3c85de45bd3fd86a8a66f7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ed1465c2469cd518a13802bf6044fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643c79923c4866289223ed6c0c80d97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2f03f58e3c85de45bd3fd86a8a66f7.png)
您最近一年使用:0次
2023高三·全国·专题练习
10 . 已知数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cb5dc920fd772fc6ec54517329b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
您最近一年使用:0次