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1、課時(shí)分層作業(yè)(十四)等比數(shù)列的性質(zhì)(建議用時(shí):40分鐘)學(xué)業(yè)達(dá)標(biāo)練一、選擇題1已知等比數(shù)列an,a11,a3,則a5等于()ABC. DC根據(jù)等比數(shù)列的性質(zhì)可知a1a5aa5.2在等比數(shù)列an中,a1a2a32,a4a5a64,則a10a11a12等于()【導(dǎo)學(xué)號(hào):91432208】A32 B16C12 D8Bq32,a10a11a12(a1a2a3)q92(2)32416.3已知等比數(shù)列an中,an0,a1,a99是方程x210x160的兩根,則a40a50a60的值為()A32 B64C256 D64B由題意得,a1a9916,a40a60aa1a9916,又a500,a504,a40a5
2、0a6016464.4設(shè)an是公比為q的等比數(shù)列,令bnan1,nN*,若數(shù)列bn的連續(xù)四項(xiàng)在集合53,23,17,37,82中,則q等于()【導(dǎo)學(xué)號(hào):91432209】A BC或 D或C即an的連續(xù)四項(xiàng)在集合54,24,16,36,81中,由題意知,這四項(xiàng)可選擇54,36,24,16,此時(shí),q,若選擇16,24,36,54,則q.5已知方程(x2mx2)(x2nx2)0的四個(gè)根組成以為首項(xiàng)的等比數(shù)列,則等于()A. B.或C. D以上都不對(duì)A不妨設(shè)是x2mx20的根,則其另一根為4,m4,對(duì)方程x2nx20,設(shè)其根為x1,x2(x10,a8a152.2公差不為零的等差數(shù)列an中,2a3a2a
3、110,數(shù)列bn是等比數(shù)列,且b7a7,則b6b8()【導(dǎo)學(xué)號(hào):91432213】A16 B14C4 D49A2a3a2a112(a3a11)a4a7a0,b7a70,b7a74,b6b8b16.3在等比數(shù)列an中,若a72,由此數(shù)列的前13項(xiàng)之積等于_213由于an是等比數(shù)列,a1a13a2a12a3a11a4a10a5a9a6a8a,a1a2a2a13(a)6a7a,而a72.a1a2a3a13(2)13213.4已知7,a1,a2,1四個(gè)實(shí)數(shù)成等差數(shù)列,4,b1,b2,b3,1五個(gè)實(shí)數(shù)成等比數(shù)列,則_.1由題意,知a2a12,b(4)(1)4.又因?yàn)閎2是等比數(shù)列中的第三項(xiàng),所以b2與第
4、一項(xiàng)同號(hào),即b22,所以1.5已知數(shù)列an的前n項(xiàng)和為Sn,數(shù)列bn中,b1a1,bnanan1(n2),且anSnn.(1)設(shè)cnan1,求證:cn是等比數(shù)列;(2)求數(shù)列bn的通項(xiàng)公式.【導(dǎo)學(xué)號(hào):91432214】解(1)證明:anSnn,an1Sn1n1.得an1anan11.2an1an1,2(an11)an1,首項(xiàng)c1a11,又a1a11,a1,c1,又cnan1,是以為首項(xiàng),公比為的等比數(shù)列(2)由(1)可知cnn1n,ancn11n.當(dāng)n2時(shí),bnanan11n1n1n1nn.又b1a1,代入上式也符合,bnn.6EDBC3191F2351DD815FF33D4435F3756EDBC3191F2351DD815FF33D4435F3756EDBC3191F2351DD815FF33D4435F3756EDBC3191F2351DD815FF33D4435F3756EDBC3191F2351DD815FF33D4435F3756EDBC3191F2351DD815FF33D4435F375