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1、2.4等比數(shù)列(一)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.掌握等比數(shù)列的定義,理解等比數(shù)列的通項(xiàng)公式及推導(dǎo)過(guò)程,并能應(yīng)用等比數(shù)列的定義及通項(xiàng)公式解決問(wèn)題.Evaluationonly.Createdwit
2、hAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.1.如果一個(gè)數(shù)列從第2項(xiàng)起,每一項(xiàng)與它的前一項(xiàng)的比等于同一個(gè)常數(shù),那么這個(gè)數(shù)列叫做________數(shù)列,這個(gè)常數(shù)叫做等比數(shù)列的________,公比通常用字母q表示(q≠0).答案:等比 公比自學(xué)導(dǎo)引Evaluati
3、ononly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.如果在a與b中間插入一個(gè)數(shù)G,使a,G,b成等比數(shù)列,那么G叫做a與b的________.答案:等比中項(xiàng)3.等比數(shù)列的通項(xiàng)公式為_(kāi)_______.答案:an=a1qn-1Eval
4、uationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.1.等比數(shù)列的公比能否為0,首項(xiàng)能否為0?答案:等比數(shù)列的首項(xiàng),公比都不為0.2.若G2=ab,則a,G,b一定成等比數(shù)列嗎?答案:不一定,因?yàn)槿鬐=0,且a,b中至少有一個(gè)
5、為0,使G2=ab,根據(jù)等比數(shù)列的定義,a,G,b不成等比數(shù)列.當(dāng)a,G,b全不為零時(shí),若G2=ab,則a,G,b成等比數(shù)列.自主探究Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.A.a(chǎn)n=a3qn-2B.a(chǎn)n=
6、a3qn-1C.a(chǎn)n=a3qn-3D.a(chǎn)n=a3qn-4解析:∵a3qn-3=a1·q2·qn-3=aqn-1=an.答案:C預(yù)習(xí)測(cè)評(píng)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.2.如果-1,a,b,c,-9成
7、等比數(shù)列,那么( )A.b=3,ac=9B.b=-3,ac=9C.b=3,ac=-9D.b=-3,ac=-9解析:∵b是-1,-9的等比中項(xiàng),∴b2=9,b=±3,又因?yàn)榈缺葦?shù)列奇數(shù)項(xiàng)符號(hào)相同,得b<0,故b=-3,而b又是a,c的等比中項(xiàng),故b2=ac,ac=9,故選B答案:BEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.
8、NET3.