TE‐18
Name:
SequencesandSeries 3.1H
Ready,Set,Go!
Ready
Topic:Findingvaluesforapattern
1. BobCooperwasbornin1900.By1930hehad3sons,allwiththeCooperlastname.By1960eachof
Bob’s3boyshadexactly3sonsoftheirown.Bytheendofeach30yeartimeperiod,thepatternofeach
Cooperboyhavingexactly3sonsoftheirowncontinued.HowmanyCoopersonswereborninthe30
yearperiodbetween1960and1990?
27
2. Createadiagramthatwouldshowthispattern.
Year
1900
1930
1960
1990
2020
#ofsons
1
3
9
27
81
3. PredicthowmanyCoopersonswillbebornbetween1990and2020,ifthepatterncontinues.
81
4. TrytowriteanequationthatwouldhelpyoupredictthenumberofCoopersonsthatwouldbeborn
between2020and2050.Ifyoucan’tfindtheequation,explainitinwords.
5. HowmanyCoopersonswereborninallfrom1900to2020?
121
Topic:FunctionNotation
Foreachofthefollowing,find , and 7.
3 2 6.
2 ,
,
,
8.
2
1
3
,
,
Completeeachtable.
9.
2nd
3rd
4th
5th
Term
1st
Value
66
50
34
18
10.
2nd
3rd
4th
5th
Term
1st
Value
3
9
27
81
SDUHSDMath1Honors
,
6th
7th
6th
8th
7th
8th
TE‐19
Set
Topic:Completingatable
Fillinthetable.Thenwriteasentenceexplaininghowyoufiguredoutthevaluestoputineach
cell.Explainhowtofigureoutwhatwillbeincell#8.
11. Yourunabusinessmakingbirdhouses.Youspend$600tostartyourbusiness,anditcostsyou$5.00
tomakeeachbirdhouse.
#ofbirdhouses
0
1
2
3
4
5
6
Totalcosttobuild
600
605
610
615
620
625
630
Explanation:Forthefirstbirdhouseitcosts$600tostartthebusiness,plus$5forthefirst
birdhouse,andafterthatitisjust$5moreforeachadditionalbirdhouse.Thecostformaking8
birdhousesisthen$
,or$640.
12. Youborrow$500fromarelative,andyouagreetopaybackthedebtatarateof$15permonth.
#ofmonths
1
2
3
4
5
6
7
Amountofmoneyowed
500
485
470
455
440
425
410
Explanation:Onmonth#1youowethetotal,$500,theneverymonthafterthatyouowe$15less
becauseyoupaid$15towardthedebtattheendofeachmonth.Onthe8thmonth,theamountof
moneyowedwouldbe
,or$395
Topic:Evaluatingequations
Evaluatethefollowingequationswhen
, , , , .Organizeyourinputsandoutputsintoa
tableofvaluesforeachequation.Letxbetheinputandybetheoutput.
14.
3
15.
3 13.
4 x
y
y
y
x
x
1
4
1
1
2
16
2
2
3
4
3
3
4
256
4
4
5
1024
5
5
SDUHSDMath1Honors
TE‐20
Go
Topic:Goodviewingwindow
Whensketchingagraphofafunction,itisimportantthatweseekeypoints.Forlinearfunctions,wewanta
windowthatshowsimportantinformationrelatedtothestory.Often,thismeansincludingboththex‐andy‐
intercepts
Findanappropriategraphingwindowforeachofthefollowinglinearfunctions.Fillintheblanks
showingtheloweranduppervaluesandincludethescaleforeachaxis.
YoumayuseanonlinegraphingutilitysuchasDesmos(https://www.desmos.com/calculator)or
MATHPAPA(https://www.mathpapa.com/calc.html?q=)
Answersmayvary.Sampleanswersprovidedbelow:
17. 7
3
14
1
16.
x:
,
byy: ,
x: , byy: , x‐scale:1 y‐scale:1
x‐scale: y‐scale: 18.
3
5
x: ,
x‐scale:1 12
byy: ,
y‐scale:1
SDUHSDMath1Honors
15
19.
x:
,
x‐scale:2 10
45
byy: ,
y‐scale:25
TE‐33
Name:
SequencesandSeries 3.2H
Ready,Set,Go!
Ready
Topic:Writetheequationofalinegiventwopoints.
Writeanequationofthelinethatgoesthroughthegiventwopoints.
1. 5, 2 and 7, 0 2. 2, 4 and 2, 6 Set
Topic:Recursiveandexplicitfunctionsofarithmeticsequences
Belowyouaregivenvarioustypesofinformation.Writetherecursiveandexplicitfunctionsforeach
sequence.Finally,grapheachsequence,makingsureyouclearlylabelyouraxes.
4. EachdayTaniadecidestodosomethingnicefor
3. 2, 4, 8, 16, …
2strangers.Writerecursiveandexplicit
equationsthatrepresentthenumberofstrangers
Taniathatdoessomethingniceforeachday(not
totalnumberofstrangers).
Recursive:
,
Explicit:
SDUHSDMath1Honors
Recursive:
,
Explicit:
TE‐34
5. Clairehas$300inanaccount.Shedecidessheis
goingtotakeouthalfofwhat’sleftinthereatthe
endofeachmonth.
6. Taniacreatesachainletterandsendsittofour
friends.Eachdayeachfriendistheninstructed
tosendittofourfriendsandsoforth.
Recursive:
,
Recursive:
,
Explicit:
Explicit:
7.
Recursive:
,
Explicit:
Topic:Summationnotationforaseries
8. Writeoutwhatismeantby:
b. ∑
a. ∑
3 9. Writethefollowinginsummationnotation:
a. 3 3 3 3
b. 2 4 6 8 10
∑
∑
10. Arethefollowingseriesequivalent?Explainyourreasoning.
and ∑
Yes.Bothsequencesrepresent:
∑
SDUHSDMath1Honors
12
⋯
TE‐35
Go
Topic:Arithmeticandgeometricsequences
Determineifthefollowingsequencesarearithmetic,geometric,both,orneither.
11. 109,94,79,64
Arithmetic
12. Christinedid41sit‐upsonTuesday,44sit‐upsonWednesday,46sit‐upsonThursday,47sit‐upson
Friday.
Neither
13. 1,9,81,729,…
Geometric
14. Whilesortingchangeintoapiggybank,Ruthput14coinsinthefirstpiggybank,14coinsinthesecond
piggybank,14coinsinthethirdpiggybank,and14coinsinthefourthpiggybank.
Both
15. 6, 24, 144, 864
Geometric
16. Abookshelfhas7shelvesofdifferentwidths.Eachshelfisnarrowerthantheshelfbelowit.Thebottom
threeshelvesare36in.,31in.,and26in.wide.Theshelfwidthsdecreasebythesameamountfrom
bottomtotop.
a. Whatisthewidthofthetopshelf?
6inches
b. Whatisthetotalshelfspaceofallsevenshelves?
147inches
SDUHSDMath1Honors
TE‐48
Name:
SequencesandSeries 3.3H
Ready,Set,Go!
Ready
Topic:Arithmeticandgeometricsequences
Findthemissingvaluesforeacharithmeticorgeometricsequence.Thensayifthesequencehasa
constantdifferenceoraconstantratio,andsaywhattheconstantdifference/rateis.
1. 5,10,15,______,25,30…
2. 20,10,______,2.5,______,…
Constantdifferenceoraconstantratio?
Constantdifferenceoraconstantratio?
ConstantDifference
ConstantRatio
Theconstantdifference/ratiois Theconstantdifference/ratiois 3. 2,5,8,______,14,_____,…
4. 30,24,_____,12,6,…
Constantdifferenceoraconstantratio?
Constantdifferenceoraconstantratio?
ConstantDifference
ConstantDifference
Theconstantdifference/ratiois
Theconstantdifference/ratiois Set
Topic:Determinerecursiveequations
Twoconsecutivetermsinanarithmeticsequencearegiven.Findtheconstantdifferenceand
therecursiveequation.
5. If 3
5and 4
8.
5
, 6
RecursiveFunction:
,
6. If 2
20and 3
12.
4
, 5
RecursiveFunction:
,
SDUHSDMath1Honors
TE‐49
Topic:Recursiveandexplicitequations
Determinewhethereachsituationrepresentsanarithmeticorgeometricsequenceandthenfindthe
recursiveandexplicitequationforeach.
7. 2, 4, 6, 8, …
8.
Time
Numberof
ArithmeticorGeometric?Arithmetic
(days)
Cells
1
5
Recursive:
,
2
8
3
12.8
4
20.48
Explicit:
ArithmeticorGeometric?Geometric
Recursive:
. ,
.
Explicit:
9. Camiinvested$6,000dollarsintoanaccount
10. Scottdecidestoaddrunningtohisexercise
thatearns10%interesteachyear.
routineandrunsatotalofonemilehisfirst
week.Heplanstodoublethenumberofmileshe
runseachweek.
ArithmeticorGeometric?Geometric
ArithmeticorGeometric?Geometric
Recursive:
,
. Recursive:
,
Explicit:
.
Explicit:
11. Vanessahas$60tospendonridesattheState
12. Michellelikeschocolatesomuchthatsheeats
Fair.Eachridecost$4.
iteverydayanditalways3morepiecesthan
thepreviousday.Sheate3piecesonday1.
ArithmeticorGeometric?Arithmetic
ArithmeticorGeometric?Arithmetic
Recursive:
,
Recursive:
,
Explicit:
Explicit:
SDUHSDMath1Honors
TE‐50
Go
Topic:Evaluateusingfunctionnotation
Findeachvalue.
13.
5 .Find 2 .
25
14.
2 .Find 3 .
15.
3 4
1 .Find 5 and 6 .
,
Topic:Solvingsystemsoflinearequations
Solvethesystemofequationsusingamatrix.
2
10
16.
4
5
, 18.
5
6
,
4
4
3
30
2
18
3
12
4
2
,
6
InfinitelyManySolutions
SDUHSDMath1Honors
7
21
3
19.
17.
TE‐61
Name:
SequencesandSeries 3.4H
Ready,Set,Go!
Ready
Topic:ConstantRatios
Findtheconstantratioforeachgeometricsequence.
1. 2,4,8,16,…
3.
, 1, 2, 4, 8, …
2.
4. 10,5,2.5,1.25,… 5, 10, 20, 40, …
Set
Topic:Recursiveandexplicitequations
Fillintheblanksforeachtableandthenwritetherecursiveandexplicitequationforeachsequence.
5. Table1
n
1
5
2
7
3
9
4
11
5
13
Recursive:
6. Table2
n
1
2
3
4
5
,
Explicit:
7. Table3
2
4
6
8. Table4
n
1
2
3
4
5
n
1
2
3
4
5
3
9
27
81
243
27
9
3
1
Recursive:
,
Explicit:
Recursive:
,
Explicit:
or
SDUHSDMath1Honors
or
Explicit:
Recursive:
,
⋅
TE‐62
Topic:Subscriptnotationforsequences
Othertextbooksmayusesubscriptnotationtowriterulesforsequences.Usetheexamplesbelowto
writetherecursiveandexplicitrulesforthefollowingsequences.
ExampleSequence FunctionNotation
SubscriptNotation
3, 5, 7, 9, …
Recursive:
Explicit:
1
3, 9, 27, 81, …
Recursive:
Explicit:
1
3,
2
3,
3 1
2
1
1 ⋅ 3
Recursive:
Explicit:
2
Recursive:
Explicit:
3,
3 3,
2
1
⋅ 3
9. 22, 19, 16, …
10. 1, 5, 25, …
,
Recursive:
,
⋅ Recursive:
Explicit:
Explicit:
Topic:Arithmeticseries
11. Findthesumofthefirst12termsofthesequence
2
10
12. Findthesum:∑
3
1
672
13. Findthesumofthefirst150termsofthesequence20,15,10,5,…
,
14. Findthesumofthefirst200evennumbers.
402,000
15. TheAgnesiHighSchoolauditoriumhasexactly26rowsofseats.Therowsarelabeled,inorder,fromthe
frontoftheauditoriumtothebackfromAthroughZ.Thereare8seatsintherowA.Eachrowafterthe
firstrowhastwomoreseatsthanthepreviousrow.Thereare10seatsinrowB,12seatsinrowCandso
on.
a. HowmanyseatsarethereinrowZ?
Thereare58seatsinRowZ.
b. WhatisthetotalnumberofseatsintheAgnesiHighSchoolauditorium?
858seats
SDUHSDMath1Honors
TE‐63
16. Thefirstfigurecontainsonesegment.Foreachsuccessivefigure,sixsegmentsreplaceeachsegment.
Thisisanexampleofafractal.
a. Howmanysegmentsareineachofthefirstfourfiguresofthesequence?
, , ,
b. Writearecursivedefinitionforthesequence.
,
⋅ Go
Topic:Graphinglinearequationsandlabelingyouraxes.
Graphthefollowinglinearequations.Labelyouraxes.
17.
4
7
18.
19.2
5
7
10
SDUHSDMath1Honors
20.
3
7
TE‐77
Name:
SequencesandSeries 3.5H
Ready,Set,Go!
Ready
Topic:Arithmeticandgeometricsequences
Foreachsetofsequences,findthefirstfiveterms.Comparearithmeticsequencesandgeometric
sequences.Whichgrowsfaster?When?
2,commondifference,d =3
1. Arithmeticsequence: 1
Geometricsequence: 1
2,commonratio,r=3
Arithmetic:
Geometric:
1
1
2
2
3
3
4
4 54
5
5
Whichvaluedoyouthinkwillbemore, 100 or 100 ?Why?
becausethevalueincreasesmuchfasterwhenmultiplyingtheprevioustermbythesame
valueasopposedtoaddingthesamevaluetothepreviousterm.
2,commondifference,d =10
2. Arithmeticsequence: 1
Geometricsequence: 1
2,commonratio,r=3
Geometric:
Arithmetic:
1
1
2
2
3
3
4
4
5
5
Whichvaluedoyouthinkwillbemore, 100 or 100 ?Why?
becausethevalueincreasesmuchfasterwhenmultiplyingtheprevioustermbythesame
valueasopposedtoaddingthesamevaluetothepreviousterm,evenifthevalueaddedismuch
largerthanthevaluemultipliedbyasseeninthisexample.
SDUHSDMath1Honors
TE‐78
Set
Topic:Arithmeticsequences
Eachofthetablesbelowrepresentsanarithmeticsequence.Findthemissingtermsinthesequence,
showingyourmethod.
3. Table1
n
1
2
3
7.5
3
12
. 4. Table2
5. Table3
6. Table4
n
n
n
1
2
1
24
1
16
2
10
2
15
2
12
3
18
3
6
3
8
4
26
4
4
4
5
0
7. Table5
n
2
3
4
5
6
27
22
17
32
12
Topic:Geometricsequences
Eachofthetablesbelowrepresentsageometricsequence.Findthemissingtermsinthesequence,
showingyourmethod.
8. Table1
n
1
2
3
3
6
12
,
SDUHSDMath1Honors
TE‐79
9. Table2
n
1
2
3
4
10. Table3
,
12. Table5
n
2
6
18
54
n
1
2
3
4
n
1
2
3
4
5
5
10
20
40
,
3
18
11. Table4
4
54
4
12
36
108
324
,
5
162
6
486
,
Go
Topic:Sequences
Determinetherecursiveandexplicitequationsforeach(ifthesequenceisnotarithmeticor
geometric,tryyourbest).Expressanswersinbothfunctionsubscriptnotation.
13. 5, 9, 13, 17, …
Thissequenceis:Arithmetic,Geometric,Neither
RecursiveEquation:
,
ExplicitEquation:
,
14. 60, 30, 0, 30, …
Thissequenceis:Arithmetic,Geometric,Neither
RecursiveEquation:
,
ExplicitEquation:
,
Thissequenceis:Arithmetic,Geometric,Neither
15. 60, 30, 15, , …
RecursiveEquation:
,
SDUHSDMath1Honors
,
⋅ ExplicitEquation:
TE‐80
16.
(Thepercentageoftilesshadedblack)
Thissequenceis:Arithmetic,Geometric,Neither
RecursiveEquation:
,
,
⋅ ExplicitEquation:
17. 4, 7, 12, 19, …
Thissequenceis:Arithmetic,Geometric,Neither
RecursiveEquation:
,
ExplicitEquation:
,
**Note:Studentsarenotexpectedtobeabletowritetherecursiveorexplicitequationsfor
question15atthispoint**
18. Writethefollowingseriesinsummationnotation:20 14 8 2 4 10
∑
19. Findthesumof∑
2 60
SDUHSDMath1Honors
TE‐87
Name:
SequencesandSeries 3.6H
Ready,Set,Go!
Ready
Topic:Comparinglinearequationsandarithmeticsequences
1. Describesimilaritiesanddifferencesbetweenlinearequationsandarithmeticsequences.
Similarities
Differences
 Linearequationsrepresentallsolutions
 Bothhaveaconsistentchangefor
toallx‐values,whereasarithmetic
everyinterval.
sequenceschooseonlyspecificvalues.
 Bothcanberepresentedasfunctions
ofavariable.
 Bothhavepointslieonaline.
Set
Topic:representationsofarithmeticsequences
Usethegiveninformationtocompletetheotherrepresentationsforeacharithmeticsequence.
Graph:
2. RecursiveEquation:
,
ExplicitEquation:
Table:
Days
Cost
1
8
2
16
3
24
4
32
CreateaContext:
Itcosts$8perdaytorentakayak.
SDUHSDMath1Honors
TE‐88
3. RecursiveEquation:
Graph:
1
4,
1
3
ExplicitEquation:
Table:
Hour
Cost
1
4
2
7
3
10
4
13
CreateaContext:
Itcostsaflatfeeof$1tocheckoutskates,and
then$3perhourfortherental.
4. RecursiveEquation:
Graph:
,
ExplicitEquation:
4 5
1 Table:
Days
Cost
1
4
2
9
3
14
4
19
CreateaContext:
ItCosts$4torentsnorkelgearonthe
firstday,andthen$5everydayafter
that.
SDUHSDMath1Honors
TE‐89
5. RecursiveEquation:
,
ExplicitEquation:
Graph:
Table:
Row
1
2
3
4
#ofseats
14
16
18
20
CreateaContext:
Janetwantstoknowhowmanyseatsare
ineachrowofthetheater.Jamalletsher
knowthateachrowhas2seatsmorethan
therowinfrontofit.Thefirstrowhas14
seats.
Topic:Applicationofarithmeticandgeometricseries
Writeaseriesrepresentationusingsummationnotationforeachscenarioandthenfindthesum.
6. Logsarestackedinapilewith24logsonthebottomrowand15onthetoprow.Thereare10rowsinall
witheachrowhavingonemorelogthantheoneaboveit.Howmanylogsareinthestack?
∑
7. Eachhour,agrandfatherclockchimesthenumberoftimesthatcorrespondstothetimeofday.For
example,at3:00,itwillchime3times.Howmanytimesdoestheclockchimeinaday?
⋅∑
8. Acompanyisofferingajobwithasalaryof$30,000forthefirstyearanda5%raiseeachyearafterthat.
Ifthat5%raisecontinueseveryyear,findthetotalamountofmoneyyouwillhaveearnedbytheendof
your5thyear.
$
,
. ∑
,
.
SDUHSDMath1Honors
TE‐90
Go
Topic:Writingexplicitequations
Giventherecursiveequationforeacharithmeticsequence,writetheexplicitequation.
9.
1
2; 1
8
10.
5
1 ; 1
0
11.
1
1; 1
SDUHSDMath1Honors
TE‐91
Name:
SequencesandSeries Review
Usethegiveninformationtostateasmuchaspossibleabouteachsequence.Youranswershouldinclude:
typeofsequence,thecommondifferenceorcommonration,atableofatleast5terms,agraph,therecursive
rule,andtheexplicitrule.
Commondifference/ratio: 3
1. Type:Arithmetic
n
1
2
2
5
3
8
4
11
5
14
Recursiverule:
Explicitrule:
1
2,
1
3
2. Type:Geometric
Recursiverule:
,
n
0
1
2
3
4
Commondifference/ratio:2
3
6
12
24
48
Explicitrule:
3∙2 SDUHSDMath1Honors
TE‐92
3. Type:Arithmetic
Recursiverule:
,
n
1
2
3
4
5
Commondifference/ratio: 2
3
5
7
9
11
Explicitrule:
4. Type:Geometric
Recursiverule:
,
n
1
2
3
4
5
40
20
10
5
2.5
CommonRatio= Explicitrule:
5.Explainhowyoutellifasequenceisarithmeticandifasequenceisgeometric.
Ifasequenceisarithmeticthereisacommondifferencethatisaddedorsubtractedfromthe
previousvaluetogetthenextvalue,whereas,ifasequenceisgeometricthereisacommonratiothat
ismultipliedbythepreviousvaluetogetthenextvalue.Inaddition,anarithmeticsequencecreates
alinearfunction,whereasageometricsequencecreatesanexponentialfunction.
SDUHSDMath1Honors
TE‐93
For#6‐8,determineifeachsequenceisarithmeticorgeometric.Findthevaluesofthenexttwo
terms.Thenwritetheexplicitandrecursiveformulasforeachsequence.
6. 90, 30, 10, , …
ArithmeticorGeometric
Next2terms: , RecursiveFormula:
,
ExplicitFormula:
7. 42, 34, 26, 18, …
ArithmeticorGeometric
Next2terms:10,2
,
ExplicitFormula:
RecursiveFormula:
8. 6, 13, 20, 27, …
ArithmeticorGeometric
Next2terms:34,41
,
ExplicitFormula:
RecursiveFormula:
9. Findthemissingtermsofthearithmeticsequencebelow.Besuretoshowallwork.
n
1
2
3
4
5
7
10. Findthemissingtermsofthegeometricsequencebelow.Besuretoshowallwork.
n
1
2
3
4
5
. 7
56
,
11. Findthemissingtermsofthegeometricsequencebelow.Besuretoshowallwork.
n
1
2
3
4
5
972
12
,
SDUHSDMath1Honors
6
18
6
6
TE‐94
12. Findthesumofthefirst50multiplesof6.
,
13. Achildbuildingatowerwithblocksuses15forthebottomrow.Eachrowhas2fewerblocksthanthe
previousrow.Supposethatthereare8rowsinthetower.
a. Howmanyblocksareusedforthetoprow?
1block
b. Whatisthetotalnumberofblocksinthetower?
64blocks
?
14. Whatisthecommonratiooftheseriesmodeledby∑
4 3
15. Howmanytermsareinthegeometricsequencehavingafirsttermof2,alasttermof32,andacommon
ratioof 2?
5terms
16. Asnailiscrawlingstraightupawall.Thefirsthouritclimbs16inches,thesecondhouritclimbs12
inches,andeachsucceedinghour,itclimbsonlythree‐fourthsthedistanceitclimbedtheprevioushour.
Assumethepatterncontinues.
a. Howfardoesthesnailclimbduringthefifthhour?
.
inches
b. Whatisthetotaldistancethesnailhasclimbedinfivehours?
.
inches
c. Expressthetotaldistancewithsummationnotation.
∑
SDUHSDMath1Honors
TE‐95
Module4HIntroductionHomework
ThefollowingproblemsareintendedforstudentstoworkonaftertheModule3HTest.Thefirstfour
problemsintroducethebeginningtasksofModule4H.Theproblemsaremeanttobedoneontheirownand
willbediscussedduringthewarmupthenextclass.Thefollowingpageisblankfortheteachertocopyand
givetoeachstudentafterthetest.Belowarethesolutionsforthechallengeproblems.
For#1‐4,createamathematicalmodelforthatincludesatable,graph,andequation:
1. Mylittlesister,Savannah,isthreeyearsold.Shehasapiggybankthatshewantstofill.Shestarted
withfivepenniesandeachdaywhenIcomehomefromschool,sheisexcitedwhenIgiveher
threepenniesthatareleftoverfrommylunchmoney.Createamathematicalmodelforthe
numberofpenniesinthepiggybankondayn.
whereprepresentsthenumberofpenniesSavannahhasandnrepresentsthenumber
ofdaysthathavepassed.
Checkfortable&graph.
2. Ourfamilyhasasmallpoolforrelaxinginthesummerthatholds1500gallonsofwater.Idecidedtofill
thepoolforthesummer.WhenIhad5gallonsofwaterinthepool,IdecidedthatIdidn’twanttostand
outsideandwatchthepoolfill,soIhadtofigureouthowlongitwouldtakesothatIcouldleave,but
comebacktoturnoffthewaterattherighttime.Icheckedtheflowonthehoseandfoundthatitwas
fillingthepoolatarateof2gallonseveryfiveminutes.Createamathematicalmodelforthenumberof
gallonsofwaterinthepoolattminutes.
.
Checkfortable&graph.
3. I’mmoresophisticatedthanmylittlesistersoIsavemymoneyinabankaccountthatpaysme3%
interestonthemoneyintheaccountattheendofeachmonth.(IfItakemymoneyoutbeforetheendof
themonth,Idon’tearnanyinterestforthemonth.)Istartedtheaccountwith$50thatIgotformy
birthday.CreateamathematicalmodeloftheamountofmoneyIwillhaveintheaccountaftermmonths.
.
Checkfortable&graph.
SDUHSDMath1Honors
TE‐96
4. Attheendofthesummer,Idecidetodraintheswimmingpoolthatholds1500gallonsofwater.I
noticedthatitdrainsfasterwhenthereismorewaterinthepool.Thatwasinterestingtome,soI
decidedtomeasuretherateatwhichitdrains.Ifoundthatitwasdrainingatarateof3%everyminute.
Createamathematicalmodelofthegallonsofwaterinthepoolattminutes.
.
Checkfortable&graph.
Module3ChallengeProblems
5. Considerthepatternofsquaregridsshown.ThesumofthenumbersinthesquaregridatStage3is27.
Ifthepatterncontinues,whatwillbethesumofthenumbersinthesquaregridatStage7?
ThesumofthenumbersattheStages1through4are1,8,27and64,respectively.Noticethat
,
,
,
.Thesesumsforma
thesenumbersareallperfectcubes:
sequencewherethenthtermofthesequenceis .Therefore,thesumofthenumbersatStage7
willbe
.
6. Thesumofalistofsevenpositiveintegersis42.Themean,medianandmodeareconsecutiveintegers,
insomeorder.Whatisthelargestpossibleintegerinthelist?
Wearetoldthatthesumofthesevenintegersis42,soitfollowsthatthesenumbershavea
.Thus,therearethreepossibilitiesfortheconsecutivemeasuresofcentral
meanof
tendency4,5and6;5,6and7;6,7and8.Butthevalues4,5and6willyieldthelargestpossible
integerinsuchalist.Sincethemeanis6,themodeandmediancouldbe4and5,respectively,
orviceversa.
Suppose,4isthemodeand5isthemedian,togetthelargestintegerwewouldhavetheseries
.Thisgivesavalueof
.
Suppose4isthemedianand5isthemode.Sincethemeandoesnotneedtobeoneoftheintegers
inthelist,togetthelargestintegerwewouldhavetheseries
.This
givesavalueof
.
Therefore,thelargestpossibleintegerinthelistis22.
SDUHSDMath1Honors