23-24高二下·全国·课前预习
1 . 知识点05等比数列的性质
1、“子数列”性质
(1)对于无穷等比数列
,若将其前
项去掉,剩余各项仍为等比数列,首项为
,公比为
;
若取出所有的
的倍数项,组成的数列仍为等比数列,首项为
,公比为
;
(2)相隔等距离的项组成的数列仍是等比数列,即
仍是等比数列,公比为 ____ ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ee88f532329c9fbc70d6c544497292.png)
2、“下标和”性质:在等比数列
中,若
,则____ ;
(1)特别地,
时,____ ;
当
时,____
(2)若数列
是有穷数列,则与首末两项“等距离”的两项的积等于首末两项的积,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ddaf21329cb1824329c296eaad5336.png)
3、两等比数列合成数列的性质:若数列
是项数相同的等比数列,
是不等于0的常数,则数列
也是____ .
1、“子数列”性质
(1)对于无穷等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
若取出所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e248261e3017741f15614caea31d0ce0.png)
(2)相隔等距离的项组成的数列仍是等比数列,即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7802fa4893785d5a8f6ea1edb8cffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ee88f532329c9fbc70d6c544497292.png)
2、“下标和”性质:在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f0c04bf4f330778a67c31371c5cf64.png)
(1)特别地,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35a47bf120bdc9294da261220947532.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865b6be02589dde9a2fb834ee7b8004b.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ddaf21329cb1824329c296eaad5336.png)
3、两等比数列合成数列的性质:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed48c3e5c53eba20c2e262b7d2c09bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e60f14235ca70ecc310820a747a548.png)
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23-24高二下·全国·课前预习
2 . 判断正误,正确的写“正确”,错误的写“错误”.
(1)在等比数列{an}中,若aman=apaq,则m+n=p+q.( )
(2)若数列{an},{bn}都是等比数列,则数列{an+bn}也一定是等比数列.( )
(3)若数列{an}是等比数列,则{λan}也是等比数列.( )
(1)在等比数列{an}中,若aman=apaq,则m+n=p+q.
(2)若数列{an},{bn}都是等比数列,则数列{an+bn}也一定是等比数列.
(3)若数列{an}是等比数列,则{λan}也是等比数列.
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3 . 已知数列
为正项等比数列,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345f68853d3b83a29419ee89e80b57d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c504030acc6ef3f9b3c8b7a2946995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
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2024-03-03更新
|
378次组卷
|
4卷引用:内蒙古自治区锡林郭勒盟2023-2024学年高三下学期开学联考理科数学试题
4 . 设
是公比不为1的等比数列,
,
,
,
成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5429ccdf44d41033cddc7ae12993a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762e892000e8cd7bd21057139658b278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478e5abb0d8b335bedffa548968eb1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e39cb81d78136387cefaa9b5f1e29d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
A.![]() | B.![]() | C.16 | D.![]() |
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5 . 已知
为等比数列,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f04f286f63962393d359510550b055b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102e44c1e2a15b201bb6386f3ce7dfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f04f286f63962393d359510550b055b.png)
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2024-02-28更新
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373次组卷
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3卷引用:河南省许平汝名校2023-2024学年高二下学期开学考试数学试题
名校
解题方法
6 . 若等比数列
的第2项和第6项分别为3和12,则
的第4项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
A.4 | B.![]() | C.6 | D.![]() |
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7 . 已知正项等比数列
中,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2c2ed37566cfdddae0fa80001844df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49637f6c115c0e9be7414157692fa128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5edade76c845f5e0e5a3aed8af3436.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-23更新
|
556次组卷
|
4卷引用:安徽省马鞍山市第二中学2023-2024学年高二上学期期末测试数学试题
安徽省马鞍山市第二中学2023-2024学年高二上学期期末测试数学试题(已下线)5.3.1 等比数列(5知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)广东省佛山市顺德市李兆基中学2023-2024学年高二下学期3月月考数学试题(已下线)4.3.1 等比数列的概念——课堂例题
解题方法
8 . 已知数列
均为正项,
且
是等差数列,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f9997226581fcb41b2fe15bafb928a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4a57cc10613c6b261ac3a8649cbdaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dea2e6db9bf2bc9ce82d3265c538979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f9997226581fcb41b2fe15bafb928a.png)
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9 . 公比不为1的等比数列
满足
,若
,则正整数m的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6245ae16d3d44e57898823c9bd92353d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de45996e6d8d75a9f136d0ec16b58ece.png)
A.11 | B.10 | C.9 | D.8 |
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10 . 在等比数列
中,
,
,则
( )
![](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/a316124e688e76d6f330ffbea49d427d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
A.14 | B.16 | C.28 | D.32 |
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