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11511:23数列知识要点回顾、常见题型配置(03)

数列知识要点回顾、常见题型配置(03)
班级 姓名 学号 (3)等比中项; 【知识要点回顾】 (1)等比数列的概念; (2)等比数列的通项公式及其性质; (3)等比数列的图像。 【常见题型配置】 一.选择题: 1. 设数列 ?an ? 为等比数列, 下列结论中, 不正确的是
2 (A) an 是等比数列





? ?

(B) ?

(C) ?lg an ? 是等差数列

(D) ?lg | an |?是等差数列

?1? ? 是等比数列 ? an ?

2. 1, a1 , a2 , a3 ,4 成等比数列,3, b1 , b2 , b3 ,5 成等差数列, 若 则 (A)

a2 ? b2





1 1 (C) ? 2 (D) ? 2 2 3. 已知等比数列 ?an ? 中,a1 ? a3 ? a5 ? 4, a7 ? a9 ? a11 ? 8 ,则 a13 ? a15 ? a17 = (
(B) ? 4. ?an ? 是公比为 2 的等比数列, a1a2 a3 ?a30 ? 2 , 设 且 那么 a3 a6 a9 ?a30 ?
30
10 15 16
20

1 2

) )

(A)12

(B)16

(C)32

(D)48



(A) 2 (B) 2 (C) 2 (D) 2 5.已知数列 ?an ? 是公差不为零的等差数列,且 a7 , a10 , a15 是一等比数列 ?bn ? 的连续三项. 若该数列的首项 b1 ? 3 , bn 可表示成 则 (A) 3 ? ( ? ) 二.填空题: 1.单调递增的等比数列 {an } 中,若 a1 ? 2 3 ? 3 2 ,则其公比 q 的取值范围是 2.若等比数列 {an } 满足 a3 ? 2a4 ? a5 ? 100,则 a4 的最大值是
2 2 2

( (C) 3 ? ( )



3 5

n ?1

(B) 3 ? ( )

5 8

n ?1

5 3

n ?1

(D) 3 ? ( )

2 3

n ?1

3. (1)数列 0.9,0.99,0.999,? 的通项公式是 (2)数列 7,77,777,7777,…的通项公式是 4.给出下列命题: ①常数列既是等差数列,又是等比数列; ②等差数列中,若公差 d ? 0 ,则数列必是递增数列; ③等比数列中,若公比 q ? 1 ,则数列必是递减数列;

; 。

a1 (1 ? q n ) ④首项为 a1 ,公比为 q 的等比数列的前 n 项和 S n ? . 1? q
其中正确命题的序号是
数列知识要点回顾、常见题型配置(03) 第 1 页 共 2 页

【知识要点回顾】等比数列的前 n 项和公式 【常见题型配置】 1.若等比数列 ?an ? 的首项为 1,公比为 q ,前 n 项和为 S n ,则数列 ? (A)

?1? ? 的前 n 项和是 ? an ?
( ( ) ) )

2.若等比数列 ?an ? 的前 n 项和 S n ? 3n ? p ,则 a1 ? a3 ? a5 ?

1 Sn

(B)

1 q
n ?1

Sn

(C) S n

(D)

Sn q n?1

(A)54 (B)182 (C)183+ P (D)42 3.已知等比数列 ?an ? 的公比 q ? 0 ,前 n 项和为 S n ,则 S 6 a7 与 S 7 a6 的大小关系是( (A) S 6 a7 ? S 7 a6 . (C) S 6 a7 ? S 7 a6 . (B) S 6 a7 ? S 7 a6 . (D)由 a1 及 q 的值而定.

4.一种细胞,每 3 分钟分裂 1 次(1 个分裂成 2 个) .把 1 个这种细胞放入容器内,经过 1 小时恰好充满容器. 如果开始时在容器内放入 2 个这种细胞,则充满容器所需要的时 间是 ( ) (A)27 分 (B)30 分 (C)45 分 (D)57 分 5.设数列 ?an ? 的前 n 项和 S n ? ar n ? b(a, b 为非零常数, r ? 0, r ? 1 ) . (1)求证:数列 ?an ? 从第二项起是等比数列; (2)若 ?an ? 是等比数列,求 a, b 应满足的关系.

6.已知数列 ?an ?, ?bn ?满足 a1 ? 1, b1 ? ? (1) a n ? 2 ?

3 1 ,且 a n ?1 ? a n ? bn , bn ?1 ? a n ? bn .求证: 2 2

1 (a n ?1 ? a n ) ; 2 (2)数列 ?an?1 ? an ? 为等比数列,并求出 ?an ?, ?bn ?的通项公式.

数列知识要点回顾、常见题型配置(03)

第 2 页 共 2 页


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