View
19
Download
1
Category
Preview:
Citation preview
14.2ArithmeticandGeometricSequences 1
Write your questions and thoughts here!
Twocommonsequencesthatappearfrequentlyinmathematicsarethearithmeticandgeometricsequences.
ArithmeticSequenceAnarithmeticsequenceisoneinwhichthesamenumberisaddedorsubtractedfromeachtermtogetthenextterminthesequence.Thenumberyouaddorsubtractiscalledthecommondifference.
Handyrulesinvolvinganarithmeticsequence:
!! = !! !! = !! + ! !! = !! + 2!!! = !! + 3!!! = !! + 4!
⋮
NthtermofanArithmeticSequenceThenthtermofanarithmeticsequencewithfirstterma1andcommondifferencedisgivenby:
!! = !! + ! − 1 !
Example1.Arethefollowingarithmeticsequences? 3,8,13,18,23,28... -2,-12,-22,-32,… 2,4,8,16,32,… 14,14.5,15,15.5,16… Example2.Giventwotermsinanarithmeticsequence,findthecommondifference,the52ndterm,andtheexplicitformula. a20
=70 a33=96
Pre-Calculus
14.2ArithmeticandGeometricSequences 2
Write your questions and thoughts here!
Time-outofforsomemathhistory….
SumofaFiniteArithmeticSequenceThesumofthefirstntermsofanarithmeticsequenceisgivenby:
!! =!(!! + !!)
2
Example3:Findthesumofthefirst20termsofthearithmeticseries:
a.2+6+10+14+18+...b.Supposethesumoftheserieshasasumof2178.FindnsuchthatSn=2178.
GeometricSequenceAgeometricsequenceisoneinwhichthesamenumberismultipliedordividedbyeachtermtogetthenextterminthesequence.Thenumberyoumultiplyordividebyiscalledthecommonratio,usuallydenotedbyr.Determineifthefollowingsequencesarearithmetic,geometricorneither.4.1,2,6,24,120,…5.81,27,9,3,1,… 6. 5,10,15,20,25,…
Example7:Thethirdtermofageometricseriesequals64whilethecommonratiois2.
a. Writearuleforthenthterm. b.Findthe9thterm
NthtermofaGeometricSequenceThenthtermofageometricsequencewithfirstterma1andcommonratiorisgivenby:
!! = !!!!!!
14.2ArithmeticandGeometricSequences 3
Write your questions and thoughts here!
Example8:Findthesumofthefirst10termsoftheseries1+5+25+125+…Example9.ForwhichtermwouldSn=3906?
SumofaFiniteGeometricSeriesThenthtermofageometricsequencewithfirstterma1andcommonratiorisgivenby:
!! = !!1− !!1− !
Recommended