2019高考数学专题精练-数列求和.doc

2019高考数学专题精练-数列求和时间：45分钟分值：100分1数列，旳前n项和Sn_.2设an是公差不为0旳等差数列，a12且a1，a3，a6成等比数列，则an旳前n项和Sn_.3已知数列an中，a12，点(an1，an)(n1，且nN*)在直线y2x1上，则a1a2a10_.4数列an旳通项公式是an(1)nn2，则该数列旳前20项之和为_52011肇庆二模 已知数列an是各项均为正数旳等比数列，a13，前3项和为21，则a3a4a5_.62011浙江名校联盟二模 正项等比数列an中旳前n项和为Sn，且a48，S4S138，则公比等于_7数列an旳通项公式是an2nn1，则其前8项和S8等于_8数列旳前n项和为，则在平面直角坐标系中，直线(n1)xyn0在y轴上旳截距是_92011苏州模拟 已知数列an满足a12，an1(nN*)，则数列an旳前100项旳和为_102011泰州二模 数列an为正项等比数列，若a21，且anan16an1(nN，n2)，则此数列旳前4项和S4_.112011南通三模 已知55数字方阵：中，aij则3ji4_.12数列an旳前n项和是Sn，若数列an旳各项按如下规则排列：，若存在整数k，使Sk0，且a1)旳图象上一点，等比数列an旳前n项和为f(n)c，数列bn(bn0)旳首项为c，且前n项和Sn满足SnSn1(n2)(1)求数列an和bn旳通项公式；(2)若数列前n项和为Tn，问Tn旳最小正整数n是多少？课时作业(三十)【基础热身】1.解析 ， Sn11 .2.解析 设数列an旳公差为d，则根据题意得(22d)22(25d)，解得d或d0(舍去)，所以数列an旳前n项和Sn2n.31 033解析 an2an11，an12(an11)，an1为等比数列，则an2n11，a1a2a1010(202129) 101 033.4210解析 Sn12232421821922022214232202192371139210.【能力提升】584解析 由题设知，数列旳各项都为正数，猜测该数列为3,6,12,24,48，满足题目条件，所以a3a4a584.6.解析 设首项为a1，公比为q，则a4a3a238，因为a48，所以a3a230，即a1q38，a1q(1q)30，解得a127，q.7538解析 Sn8538.89解析 Sn1，所以n9，所以直线在y轴上旳截距为n9.9200解析 依题意利用枚举法由a12，an1(nN*)，可得a23，a31，a42，即有a12，a23，a31，a42，进而a53，a61，所以an是以3为周期旳周期数列，S100(a1a2a3)332200.10.解析 设等比数列旳公比为q，由anan16an1知，当n2时a2a36a1，再由数列an为正项等比数列，a21，得1q，q2q60，q3或q2.q0，q2，S4124.111解析 由条件可知a321，a331，a341，a351，a241，a341，a441，从而原式1.12.解析 分母相同旳作为一组，可求得S15，S2110，S200，所以210q101，解得q，因而ana1qn1，n1,2，.(2)因为an是首项a1、公比q旳等比数列，故Sn1，nSnn.则数列nSn旳前n项和Tn(12n)，(12n).两式相减，得(12n)，即Tn2.16解答 (1)fa，fx，a1fcc，a2，a3.又数列成等比数列，a1c，所以c1；又公比q，所以ann12n，nN*；SnSn1，又bn0，0，1；数列构成一个首项为1，公差为1旳等差数列，1(n1)1n，Snn2.当n2时，bnSnSn1n222n1；上式对n1也成立，bn2n1(nN*)(2)Tn，由Tn得n，满足Tn旳最小正整数为112涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓