2020-2021学年高二数学单元测试定心卷
数列(基础过关)
一、单项选择题:本题共8小题,每小题5分,共40分.在每小题给出的四个选项中,只有一个选项是符合题目要求的.
A.8 | B.12 | C.16 | D.24 |
【知识点】 等差数列通项公式的基本量计算
A.2 | B.3 |
C.4 | D.5 |
【知识点】 等比数列通项公式的基本量计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e449a6d9e76e0497bf2672740f801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7381ec8d8f097e681b6d2453bf4f5bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84784de25156b20dbe91f4397495bb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 等差数列通项公式的基本量计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d76772d78168f69897ad5a78db14fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9113cddac0d0ae8998914821a442b9d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 等差数列前n项和的基本量计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ab55b69404fdbda2a9e7591ac4f309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fcb0cb28af1225ea8fca9104e6960a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa906e7ed27950fca3b2edabfd31fccf.png)
A.12 | B.24 | C.30 | D.32 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2030a7c508abe4b2a03bc702cf7692d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6567511bb9486b2ca7452b870abd2a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d01dd350dc95f42f1883e0cc7aae084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
【知识点】 数列-复利
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac577f987d768e1a115f2747ec0fd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c622a7e9276bddc0d80d4ebc3445f37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8319c7a0514be9c6eab2d27adea1900e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
A.有最大项,有最小项 | B.有最大项,无最小项 |
C.无最大项,有最小项 | D.无最大项,无最小项 |
【知识点】 确定数列中的最大(小)项
二、多项选择题:本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求,全部选对的得5分,部分选对的得3分,有选错的得0分.
A.按一定次序排列的一列数叫做数列 |
B.若{an}表示数列,则an表示数列的第n项,an=f(n)表示数列的通项公式 |
C.同一个数列的通项公式的形式不一定唯一 |
D.同一个数列的任意两项均不可能相同 |
【知识点】 数列的概念及辨析
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d9d7b447de1b74707bb283e4c98f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 等比数列的定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95b09ff605c83c8e57f74fb4ec5e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
【知识点】 由前n项和判断数列是否是等差数列 由Sn求通项公式
三、填空题:本题共4小题,每小题5分,共20分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab44bab7d586b371efa34f321301615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acbca4dcc52c40a4812256252367728.png)
【知识点】 等比数列下标和性质及应用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6de24101eb69b251596bbf8da18f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed88494a1c51daa92014abbc34c266e.png)
【知识点】 等比数列通项公式的基本量计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c96873a5936624c495460da28843dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfb8091a44e1edbc4dc5274a57cbd0b.png)
四、解答题:本题共6小题,共70分.解答应写出文字说明、证明过程或演算步骤.
(1)9,99,999,9 999,…;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b77a750c8b127476bbb41e1eb289750.png)
【知识点】 观察法求数列通项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4917b8dd58509551fb04a9081861ea3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
【知识点】 等差数列通项公式的基本量计算 求等比数列前n项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770764f4a9db94b71a45b2774595fd01.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac26e75b047caf53e9d14db0ffe8e48.png)
【知识点】 写出等比数列的通项公式 等比数列前n项和的基本量计算
![](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/20210b321be585d32e425a6a4de3ca73.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
【知识点】 判断或写出数列中的项 利用定义求等差数列通项公式 构造法求数列通项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8ac883e5d7f26bfe11704862f108d9.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
【知识点】 由Sn求通项公式 二次函数法求等差数列前n项和的最值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1720502485a01901c71a2229b6b3d746.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设bn=log3a1+log3a2+…+log3an,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
【知识点】 写出等比数列的通项公式 等比数列通项公式的基本量计算 裂项相消法求和