INFINITESEQUENCESANDSERIESChapter910.1SEQUENCESAsequencecanbethoughtofasalistofnumberswritteninadefiniteorder:a1,a2,a3,…,an,…Thenumbera1iscalledthefirstterm,a2isthesecondterm,andingeneralanisthen-thterm.Wewilldealexclusivelywithinfinitesequencesandsoeachtermwillhaveasuccessoran+1.NOTATIONThesequence{a1,a2...
Sequences and Series (3) Sequences and Series (3) Learn how to calculate Learn how to calculate THE SUM OF TERMS IN A THE SUM OF TERMS IN A ARITHMETIC SEQUENCE ARITHMETIC SEQUENCE The can pyramid… The can pyramid… How many cans are there in this pyramid. How many cans are there in...
e.g.1Givethe1sttermandwritedowna recurrencerelationforthesequence 1,4,16,64,...Solution:1stterm:Recurremcerelation:u11un14un Otherlettersmaybeusedinsteadofuandn,sotheformulacould,forexample,begivenas ak14ak SequencesandSeriesRecurrenceRelationse.g.2Writedownthe...
INFINITESEQUENCESANDSERIES 10.1SEQUENCES Asequencecanbethoughtofasalistofnumberswritteninadefiniteorder:a1,a2,a3,…,an,…Thenumbera1iscalledthefirstterm,a2isthesecondterm,andingeneralanisthen-thterm.Wewilldealexclusivelywithinfinitesequencesandsoeachtermwillhaveasuccessoran+1.NOTATIONThesequence{a1,a2,a3...
12.3 – Geometric Sequences and Series Arithmetic Series Sum of Terms Geometric Series Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term Vocabulary of Sequences (Universal) Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 –...
Chapter3SequencesandSeries(PartB)Topics GeometricProgressionTheBinomialExpansion 2 GeometricProgression Ingeneral,ageometricprogressioncanbewrittenas:(n−1)a,ar,ar,KK,ar 2 ,KK wherea=thefirsttermr=thecommonratio 3 GeometricProgression Thenthterm,un=ar(n−1)Thesumofthefirstnterms,a(rn−1)Sn=...
Geometric Sequences and Series 国际象棋起源于古印度,关于国际象棋还有一个传说。国王奖赏发明者,问他有什么要求,他答道:“在棋盘第一个格放1颗麦粒,在第二个格放2颗麦粒,在第三个格放4颗麦粒,在第四个格放8颗麦粒。以此类推,每个格子放的麦粒数是前一个格子的2倍,直到64个格子。国王觉得这太容易了,就...
Geometric Sequences and Series 9.3GeometricSequencesandSeries Objective •Tofindspecifiedtermsandthecommonratioinageometricsequence.•Tofindthepartialsumofageometricseries GeometricSequences •Consecutivetermsofageometricsequencehaveacommonratio.DefinitionofaGeometricSequence •Asequenceisgeometriciftheratiosof...
CHAPTER 4_SequenceSeries CHAPTER4 SEQUENCESANDSERIES 4.1 SEQUENCE Considerthefollowingsequence:Sequence1Sequence22,4,6,8,102,4,6,8,10…..1st2nd3rd4th5thtermtermtermtermterm1st2nd3rd4th5thtermtermtermtermterm Finitesequenceendafteracertainno.ofterms.Infinitesequenceisonethatcontinuesindefinitely(nonstop)...
ArithmeticSequencesandSeriesArithmeticSequence Asequenceisarithmeticif eachterm–thepreviousterm=dwheredisaconstante.g.Forthesequence 2,4,6,8,...d=2ndterm–1stterm =3rdterm–2ndterm...=2 The1sttermofanarithmeticsequenceisgiven thelettera.ArithmeticSequencesandSeriesArithmeticSequenceAnarithmeticsequenceisof...