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1、Chapter12ArithmeticandGeometricsequences(等差及等比数列)ThesyllabusWholeSyllabusTailoredSyllabusInsertionofarithmeticandgeometricmeans(等差及等比中项).Sumtonterms(n项和).Sumtoinfinity(无限项之和)ofgeometricsequences.Applicationstoeverydaylifeproblems.Sumtonterms.Sumtoinfinityofgeometricsequences.Applicationstoeverydayli
2、feproblems.(A)Sequences(数列)Definition:Asequenceisagroupofnumbersorderedinaspecifiedway.Symbolsandterms:T(1),T(2),T(3),...,T(n),....1stterm,2ndterm,3rdterm......,nthterm(第n项)GeneralTerm(通项)(B)Series(级数)Definition:Aseriesisthesumofthetermsofasequenceinthefollowingway.T(1)+T(2)+T(3)+....+T(n)+...Thesum
3、ofthefirstntermsisdenotedbyS(n)=T(1)+T(2)+...+T(n)(C)ArithmeticSequences(等差数列)(I)Definition:Ifasequenceisintheform+d+d+d+d................T(1),T(2),T(3),............................,T(n),....,a,a+d,a+2d,...........................,a+(?)d,...,thenitiscalledanArithmeticSequence,where19aistheFirstterm(
4、首项)anddistheCommonDifference(公差).Note:ArithmeticSequenceisalsocalledArithmeticProgression(A.P.)..........................(1)T(n)=a+(n-1)d(nthterm/Generalterm)(II)ArithmeticSeries(等差级数)Sumofthefirstnterms(n项和):S(n)=T(1)+T(2)+T(3)+...+T(n)=a+(a+d)+(a+2d)+...+[a+(n-1)d].........................(2).....
5、....................(3)(Sumtonterms)whereaistheFirsttermanddistheCommonDifference.(III)ArithmeticMeans(等差中项)(i)Ifa1,a2,a3,a4,a5areinArithmeticSequence,thena2,a3,a4aretheArithmeticMeansbetweena1anda5.插入等差中项属剪裁课程以外。Note:Ifa1=a,thena2=a+d,a3=a+2d,a4=a+3d,a5=a+4d,wheredisthecommondifference.(ii)Ifa,b,ca
6、reinarithmeticsequence,thentheArithmeticMeanisbandisgivenby.........................(4)Note:c-b=b-a=commondifference19(D)GeometricSequences(等比数列)(I)Definition:Ifasequenceisintheform´r´r´r´r................T(1),T(2),T(3),............................,T(n),....,a,ar,ar2,..............................,a
7、r(?),......,thenitiscalledaGeometricSequence,whereaistheFirstterm(首项)andristheCommonRatio(公比).Note:GeometricSequenceisalsocalledGeometricProgression(G.P.)..........................(5)(nthterm/Generalt
