高二數(shù)學(xué)高二數(shù)等學(xué)比數(shù)列

1.三角形的三邊成等比數(shù)列，求公比q的取值范圍.解：設(shè)三邊為：a,aq,aq2(a,q>0)，則解(1)得：解(2)得：解(3)得：qR求它們的交集故公比q的取值范圍：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.小結(jié)：等比數(shù)列{an}的三種判定方法思考題：已知四個數(shù)，前三個數(shù)成等比數(shù)列，它們的和19，后三個數(shù)成等差數(shù)列，它們的和12，求這四個數(shù)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.性質(zhì)：（1）an=amqn-m（2）若m+n=p+k，則am·an=ap·ak,（1）若a1a9=64，且a3+a7=20，則a11=________（2）若a7·a12=5，則a8·a9·a10·a11=_________更多資源

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.A.成等差數(shù)列不成等比數(shù)列B.成等比數(shù)列不成等差數(shù)列C.成等差數(shù)列又成等比數(shù)列D.既不成等差數(shù)列又不成等比數(shù)列Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.A.等比數(shù)列，但不是等差數(shù)列B.等差數(shù)列，但不是等比數(shù)列C.等差數(shù)列，而且也是等比數(shù)列D.非等差數(shù)列又非等比數(shù)列Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.所以{bn}是以3為首項，2為公比的等比數(shù)列Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.設(shè)等比數(shù)列{an}，判斷下列結(jié)論的正誤Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.(10)等比數(shù)列的增減性：

當(dāng)q>1，a1>0或0<q<1，a1<0時,{an}是遞增數(shù)列

當(dāng)q>1，a1<0或0<q<1，a1>0時,{an}是遞減數(shù)列當(dāng)q=1時，{an}是常數(shù)數(shù)列

當(dāng)q<0時，{an}是擺動數(shù)列Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.已知(b-c)logmx+(c-a)logmy+(a-b)logmz=0(1)設(shè)a,b,c等差數(shù)列，且公差不為零，求證：x,y,z成等比數(shù)列(2)設(shè)正數(shù)x,y,z成等比數(shù)列，且公比不為1求證：a,b,c成等差數(shù)列Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.典例1：在1與2之間插入n個正數(shù)a1，a2，a3，…，an，使這n+2個數(shù)成等比數(shù)列；又在1與2之間插入n個正數(shù)b1，b2，b3，…，bn，使這n+2個數(shù)成等差數(shù)列．記An＝a1a2a3…an，Bn＝b1+b2+b3+…+bn．求數(shù)列{An}和{Bn}的通項Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.典例2設(shè)數(shù)列{an}的首項a1＝t，前n項和Sn滿足；5Sn-3Sn-1＝3，(n≥2，n∈N)是否存在常數(shù)t，使得數(shù)列{an}為等比數(shù)列，若存在，求出t的值，若不存在，請說明理由更多資源

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.典例3三個互不相等的數(shù)成等差數(shù)列，如果適當(dāng)排列這三個數(shù)，也可以成等比數(shù)列，已知這三個數(shù)的和等于6，求此三數(shù)．Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.典例4已知正項等比數(shù)列{an}中，a1a5+2a2a6+a3a7＝100，a2a4-2a3a5+a4a6=36求數(shù)列的通項公式Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile.Copyright2004-2011AsposePtyLtd.1.已知數(shù)列l(wèi)gx+lgx2+lgx3+…+lgx1