23-24高二上·全国·课后作业
1 . 斐波那契数列
满足条件:
,
.按如下步骤将
分解为两个等比数列
,
之和,最后可以得出
的通项公式:
(1)若等比数列
满足条件
,求
的公比q.
(2)若等比数列
,
同时满足条件
,
,且
,求
和
的通项公式.
(3)设
,试写出斐波那契数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7885a0090b2cab1a7501209f691747c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69d323ae24f4de27d776747f798a0b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.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/644f94297a84a8edbda26f1e408444e1.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316b5d6779890069e877f081d1833883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若等比数列
![](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/316b5d6779890069e877f081d1833883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288f806f407bee75166d2c43f3c63ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fb00be16d6ca922baa52ae69988c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083f9364e291ac5d5f7af1ee93f0a732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
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21-22高二·江苏·课后作业
2 . 判断下列数列是否为等比数列:
(1)1,2,1,2,1;
(2)-2,-2,-2,-2;
(3)1,
,
,
,
;
(4)2,1,
,
,0;
(5)
,
,
;
(6)1,-1,1,-1.
(1)1,2,1,2,1;
(2)-2,-2,-2,-2;
(3)1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158b045c6172c4178d7aa52083e1489f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4924aedda5d82685e31b85516e7105a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54da42446de9129bc86246497e676eaa.png)
(4)2,1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47beab88f3c7978932f2e13824d60191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930f7706c8f0a021d2e81f1cba24cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c706203c5897e3e5cf328b8b35cc3ef.png)
(6)1,-1,1,-1.
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3 . 已知等比数列
的公比
,前
项和为
.证明
,
,
成等比数列,并求这个数列的公比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354efd9145bb3bd889cf0eaadbcc55f2.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5188d6760683a860adab0cda195cdf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6fe11dfa538e67bfd63478fc428a1.png)
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2023-09-19更新
|
179次组卷
|
2卷引用:人教A版(2019)选择性必修第二册课本例题4.3 等比数列
4 . 已知
是各项均为正数的等比数列,公比为q,求证:
是等比数列,并求该数列的公比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c133f850a40f4d23c30fa91a1e7d74a2.png)
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5 . 判断下列数列是否为等比数列:
(1)9,0.9,0.09,0.009;
(2)
,
,
,
;
(3)
,
,
,
;
(4)
,
,
,
.
(1)9,0.9,0.09,0.009;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b57c4a905b766f8755d01b28d22a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993908fc9c1baaf8774ba080107c23d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd7d7624d5efbb189205bd3a4a13e3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bac900bd09df30926bbf18dcf94628a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5498db3231db49529b93fdf13433298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f5ca7640f5202cc27dd03190d101e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6e41b8e683c5d3b71c867b582524a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a9b9cada684621f0b080058a3582d3.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef25f1fa9539e95e763cd0ef4bf68782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b4d1868e26d04a2bd6b30a07d514c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3e49942ad60434e5ea393f722be9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425c4c772403a5d629255d864fe9abf4.png)
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6 . 图中的一系列三角形图案称为谢尔宾斯基三角形.在图中4个大三角形中,着色的三角形的个数依次构成一个数列的前4项,写出这个数列的一个通项公式.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/42933c4a-7c6d-4f77-8c98-d39a6d95eaef.png?resizew=545)
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7 . 存在数列既是等差数列又是等比数列吗?如果存在,试举出实例;如果不存在,说明理由.
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20-21高二·全国·课后作业
8 . 某制糖厂第一年制糖5万吨.如果平均每年的产量比上一年增加10%,那么从第一年起,约几年内可使总产量达到30万吨(保留到个位)?(参考数据:
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcea73811a794f4e4ef9f140e76784a9.png)
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9 . 在等比数列中,公比
为什么不为0?能否有某一项为0?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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2023-10-11更新
|
83次组卷
|
2卷引用:北师大版(2019)选择性必修第二册课本习题第一章3.1 等比数列的概念及其通项公式
10 . 已知一个等比数列
的首项为
,公比为q.
(1)将
的前m项去掉,其余各项依次构成的数列还是等比数列吗?如果是,它的首项与公比分别为多少?
(2)取出
的所有奇数项,依次构成一个新的数列,这个数列还是等比数列吗?如果是,它的首项与公比分别为多少?
(3)取出
的所有项数为5的倍数的各项,依次构成一个新的数列,这个数列还是等比数列吗?如果是,给出证明并求出首项与公比;如果不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)取出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)取出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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