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Understanding Sequences for Speed and Profit Analysis

Explore sequences in speed zones and profit growth, analyzing crash data, profit patterns, geometric and arithmetic sequences, distinguishing sequence types, and calculating terms.

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Understanding Sequences for Speed and Profit Analysis

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  1. Topic i. numbers & algebra Subtopic: SEQUENCES

  2. FACT: In a 60 kph speedzone, therisk of casualtycrashdoubles forevery 5 kph overthespeedlimit.

  3. FACT: In averageconditions, a car travelling at 60 km/h willtakeabout 45 metres to stop in anemergencybrakingsituation. A car brakingfrom 65 km/h willstillbemoving at closeto 32 km/h after 45 metres travelled.

  4. EXAMPLE 1. CRASH DATA

  5. Howmuchspeeddoesthe driver succeed in losingbeforeimpact?

  6. Each 5 kph added to the initial speed results in an approximately 20% decrease in the amount of speed the driver manages to lose by braking. WHY IS THIS????

  7. Each 5 kph added to the initial speed results in an approximately 20% decrease in the amount of speed the driver manages to lose by braking. WHY IS THIS???? - 18% - 32% - 25% - 19% - 29% - 17%

  8. EXAMPLE 2. PROFIT A companybegandoingbusinessfouryears ago. Itsprofitsforthelastfouryearshavebeen$11 million, $15 million, $ 19 millionand $23 million. IfthePATTERNcontinuestheexpectedprofit in 30yearsisgoingtobe $127 million WHY????

  9. EXAMPLE 3. SQUARES & SQUARE NUMBERS HOW MANY POINTS WILL THE NEXT FIGURE HAVE? WHY??? WHAT ARE THESE SQUARES REPRESENTING????

  10. All of the above are …

  11. SEQUENCES

  12. SEQUENCES But … WHAT IS A SEQUENCE?

  13. DEFINITION A SEQUENCEis a set of quantitiesarranged in a definiteorder. Forexample: • 1, 2, 3, 4, 5, … • 1, 4, 9, 16, 25, … • 1, 8, 27, 64, 125, … • -10, -8, -6, -4, -2, …

  14. TWO TYPES OF SEQUENCES • Arithmetic Sequence • Geometric Sequence

  15. TWO TYPES OF SEQUENCES ArithmeticSequence 1, 3, 5, 7, 9, … 11, 15, 19, 23, … GeometricSequence 2, 6, 18, 54, 162 200, 20, 2, 0.2

  16. Howtodistinguishanarithmetic series? An arithmetic sequence will always have a common difference between successive terms. For example: • 2, 4, 6, 8, 10, … COMMON DIFFERENCE of 2 • 1, 4, 7, 11, 14, … COMMON DIFFERENCE of 3

  17. GETTING BACK TO THE PROFIT EXAMPLE … How can youcalculatethe 27thterm? Moreover, how can youcalculatethenthterm? Tip: Whatisthecommondifference?

  18. GETTING BACK TO THE PROFIT EXAMPLE … The common difference is 4. 15 – 11 = 4 19 – 15 = 4 Therefore we know that we need to multiply the nth by 4

  19. GETTING BACK TO THE PROFIT EXAMPLE … But … 4(1) = 4, 4(2) = 8 and 4(3) = 12 … Ifweadd + 7 we’llgettheresult. Hence, in 30 yearstheprofitwillbe 30(4) + 7 =

  20. HOW WOULD YOU CALCULATE THE Nth TERM???

  21. HOW WOULD YOU CALCULATE THE Nth TERM??? Tip: Look forit in yourbooklet!!!!!

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