数列求和综合练习题
一、选择题
1.已知数列?an?的前n项和为Sn,若an?1n?n?1,Sn?10,则n?( )
A.90 B.121 C.119 D.120
2.已知{an}是公差为1的等差数列,Sn为{an}的前n项和,若S8?4S4,则a10?( ) A.
1719 B. C.10 D.12 223.数列?an?中,a1??60,an?1?an?3,则此数列前30项的绝对值的和为 ( )
1,则S6等于( )
n(n?1)A.720 B.765 C.600 D.630 4.数列{an}的前n项和为Sn,若an?A.
1456 B. C. D. 425675.设{an}是由正数组成的等比数列,Sn为其前n项和.已知a2·a4=1,S3=7,则S5=( ) A.
1311715 B. C. D. 2422是等差数列
的前项和,已知
,则
等于 ( )
6.设
A. 13 B. 35 C. 49 D. 63
7.等差数列{an}的前n项和为Sn,a5?11,S12?186,则a8= ( ) A.18 B.20 C.21
D.22
8.等差数列{an}的前n项和为Sn,且S3?6,a3?0,则公差d等于( ) A.?1 B.1 C.?2 D.2
9.设等差数列?an?的前n项和为Sn,若a1??11,a4?a6??6,则当Sn取最小值时,n等于( ) A.6 B.7 C.8 D.9 10.在等差数列
{an}中,已知
a4?a8?16,则该数列前11项的和
S11等于( )
A.58 B.88 C.143 D. 176
n?111.已知数列{an}的前n项和为Sn?1?5?9?13?17?21???(?1)(4n?3),则S15?S22?S31的
值是( )
A.-76 B.76 C.46 D.13
12.等比数列{an}的前n项和为Sn,若a1+a2+a3+a4=1,a5+a6+a7+a8=2,Sn=15,则项数n为( ) A.12 B.14 C.15 D.16
13.等差数列?an?中,若a1?a4?a7?39,a3?a6?a9?27,则?an?的前9项和为( ) A.297 B.144 C.99 D.66
试卷第1页,总4页
二、解答题
14.已知数列?an?的前n项和Sn?n2,n?N*. (1)求数列?an?的通项公式;
(2)若数列?bn?是等比数列,公比为q?q?0?且b1?S1,b4?a2?a3,求数列?bn?的前n项和Tn.
15.已知等差数列?an?的前n项和为Sn,且S3?9,a1,a3,a7成等比数列. (1)求数列?an?的通项公式;
(2)若数列?an?的公差不为0,数列?bn?满足bn?(an?1)2,求数列?bn?的前n项和Tn.
n??
n+116.设数列?an?的前n项和Sn=2-2,数列?bn?满足bn?1.
(n?1)log2an(1)求数列?an?的通项公式; (2)求数列?bn?的前n项和Tn.
17.已知数列{an}的各项均为正数,Sn是数列{an}的前n项和,且4Sn?an?2an?3. (1)求数列{an}的通项公式;
n(2)已知bn?2,求Tn?a1b1?a2b2???anbn的值.
2
试卷第2页,总4页
n18.已知数列{an}的前n项和Sn?2,数列{bn}满足b1??1,bn?1?bn?(2n?1) ?n?1,2,3,L?.
(1)求数列{an}的通项an; (2)求数列{bn}的通项bn; (3)若cn?
19.已知数列?an?的前n项和为Sn,且2Sn?n?n.
2an?bn,求数列{cn}的前n项和Tn. n(1)求数列{an}的通项公式; (2)若bn?
20.已知数列{an}的前n项和Sn?2?an,数列{bn}满足b1=1,b3+b7=18,且bn?1?bn?1?2bn(n≥2).(1)求数列{an}和{bn}的通项公式;(2)若cn?
21.已知数列{an}的前n项和为Sn,数列{Sn?1}是公比为2的等比数列,a2 是a1和a3的等比中项. (1)求数列{an}的通项公式; (2)求数列nan的前n项和Tn.
1?2an?1,(n?N*)求数列{bn}的前n项和Sn.
anan?1bn,求数列{cn}的前n项和Tn. an??试卷第3页,总4页
数列求和综合练习题(含答案)
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