Geometric Sequences

Geometric Sequences - www.mathhefionsa Geometric Sequences...

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Unformatted text preview: www.mathhefionsa Geometric Sequences The Hardware Store Credit Card Secret: EAlomlhardwarestoregivesyonnneyearmpayyourbill. Attheendofoneyearyoumustpay : your bill orbe charged 28.3% interest onyourdeht. Let‘s assume you do notpayyourbill for 10 years. Studythe table to View this fascinating geometric sequeLce Moe m1 sea: near a me ms Alan-6 Afler? ma liners mm year years years years years years years years years years 51'5"” mas 51559 52131 32752 53545 $4566 35am $1514 39755 $12555 nnnnannnfinnnnn Since the $1000 balancewas notpaid ofl’, the year end balance' {5 multiplied by 1. 288 every year. i This pattern will continue indefinitely unfl the balance” 15 paid. Understanding geometric : sequences is important for understanding your personal finances \flflbhflbfihflfiflflflhflbfihhfiflflflhfl A geometric sequence is a group of numbers that Is created when the previous number Is multiplied by a oonunon ratio. For example 4,8,16,32,64 is a metric sequence with 5 terms. The common ratio for 4,8,16,32,64 is 2 and the common ratio for 100,50,25,... is 0.5. lore 113. Given the geometric sequence, 10. 20. 40.. 1E1.4 Given the geometric sequence, 10, 20, determine megfitermbyany method. 5' determinethe 22ml yawn. 3,5: amass: *1 *1 are {Finn- W5 War-q. [0,10 «40 so Ibo 52.0 sea {29%; he: l0 (3 ‘tn-n 3.560 : Bel 115.Create a formula that could be used to find any term in any geometric sequence; 3,15,12,24 .... Complete the table below Page ZSEWEW mmimnbmmm. [Mwithpuulsafon Denatuaeafier1m2013 www.mathhefionsa The Geometric Sequence Formula t =t rn-l This formula finds flail of terms a-Fitst term " ‘ theflth term This form‘dawfllfindmewterm. 9 4x1 4x2 _—— 116. Explain what each part :3me geometric sequence fonnula means. _ n—l g_gr 4'?) Detflfid ether each string afnumbers £5 geometric. If it is slate the general term: 6” = ter) 117.2 .9' 7 E 1135.10.20.40... _ *&.x= Fm K5 __ "'4 '— 115 I E n-«I {Ln- 5(3) Eta: ’WIEY-{gfint ("ll/"1) o :- :3 H D .3 I-l .3 H .9 I“ _- 58:. i J'- F F ,2 121.challenge: Given the geometric sequence, 3,6,12,24,... determine the 101k term. 11 -( =1g=1 tart: rIn we?” 325-31" = 536.: Page ZTIWEW mmtmmwmmmmmmlmzm www.mathhefionsa Find the term. 122.01ven: i 123.6iven: 5. 15.45,... i 124.Given: 20400. E 125.Given: 3,-9.27.—81.. 3.6.1224, Entity. ' 10240, 5120,...find find 1-,, find ’10- r15. lhefmmula 1:. = 0‘“ Filontlbmuh in =31239 rm = 1536 no new 9 1536 A credit uni company charges 18% interest per year on all unpaid balances. David has an outstanding balance of $1000. Determine the amount owing alter each of the following time periods. I": i . l ‘5 126.Without using amicuiator. E 127.1year —-7 aia¥um I 123.2yeau's guesshcwlong 1: willtake 5 E Dawd’s debt to 5 ' double? 5 . 129% green E 130.8 years E 13LApproxunateiy how long does E E it take for David”: debt to E E double? 132.1'he Rule of 72. This Is quick business calculation that determines-bow quickly an monument or debt wili doubles” specific interest rate Simply divide 72 by the Interest rate. The quotleotis the time period it takes to double. Confirm that. this is true with 18%. 133.8HALLENGE: Find the column moo. 134.. Challenge: How many terms are in the foliowi ce uence: 3,6,12,24...49152. £33.32- “3 " Page HIWEW Cmflditmthbmunmlhewfihmmmtmefiulmzml ...
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