等差数列练习题(一)1.已知为等差数列,,则等于A.-1B.1C.3D.7【解析】∵135105aaa即33105a∴335a同理可得433a∴公差432daa∴204(204)1aad.选B。【答案】B2.设nS是等差数列na的前n项和,已知23a,611a,则7S等于()A.13B.35C.49D.63故选C.3.等差数列{}na的前n项和为nS,且3S=6,1a=4,则公差d等于A.1B53C.-2D3【答案】:C[解析]∵31336()2Saa且3112=4d=2aada.故选C4.已知na为等差数列,且7a-24a=-1,3a=0,则公差d=A.-2B.-12C.12D.2【解析】a7-2a4=a3+4d-2(a3+d)=2d=-1d=-12【答案】B5.若等差数列{}na的前5项和525S,且23a,则7a()A.12B.13C.14D.15答案B6.在等差数列na中,284aa,则其前9项的和S9等于()A.18B27C36D9答案A7.已知{}na是等差数列,124aa,7828aa,则该数列前10项和10S等于()A.64B.100C.110D.120答案B8.记等差数列{}na的前n项和为nS,若112a,420S,则6S()A.16B.24C.36D.48答案D9.等差数列na的前n项和为xS若=则432,3,1Saa()A.12B.10C.8D.6答案B10.设等差数列{}na的前n项和为nS,若39S,636S,则789aaa()A.63B.45C.36D.27答案B11.已知等差数列}{na中,12497,1,16aaaa则的值是()A.15B.30C.31D.64答案A12.已知等差数列na的前n项和为nS,若1221S,则25811aaaa.答案7二、填空题13.设等差数列na的前n项和为nS,若972S,则249aaa=答案241解析na是等差数列,由972S,得599,Sa58a2492945645()()324aaaaaaaaaa.14.设等差数列na的前n项和为nS,若535aa则95SS解析na为等差数列,9553995SaSa答案915.等差数列na的前n项和为nS,且53655,SS则4a解析∵Sn=na1+12n(n-1)d∴S5=5a1+10d,S3=3a1+3d∴6S5-5S3=30a1+60d-(15a1+15d)=15a1+45d=15(a1+3d)=15a4答案3116.已知等差数列的公差是正整数,且a,则前10项的和S=答案:-10三、解答题17.在等差数列中,,,求.解答、,18、设等差数列的前项和为,已知,>,<,①求公差的取值范围;②中哪一个值最大?并说明理由.①∵,∴解得,,②由,又∵∴是递减数列,∴中最大.20、设等差数列的前n项的和为Sn,且S4=-62,S6=-75,求:(1)的通项公式an及前n项的和Sn;(2)|a1|+|a2|+|a3|+……+|a14|.解:设等差数列首项为a1,公差为d,依题意得解得:a1=-20,d=3。⑴;⑵∴.2