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Arithmetic and Geometric Sequences. Arithmetic Sequences Every day a radio station asks a question for a prize of $150. If the 5th caller does not answer.

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Presentation on theme: "Arithmetic and Geometric Sequences. Arithmetic Sequences Every day a radio station asks a question for a prize of $150. If the 5th caller does not answer."— Presentation transcript:

1 Arithmetic and Geometric Sequences

2 Arithmetic Sequences Every day a radio station asks a question for a prize of $150. If the 5th caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question.

3 Arithmetic Sequences Make a list of the prize amounts for a week (Mon - Fri) if the contest starts on Monday and no one answers correctly all week.

4 Arithmetic Sequences Monday : $150 Tuesday: $300 Wednesday: $450 Thursday:$600 Friday:$750

5 Arithmetic Sequences sequence arithmetic sequence add These prize amounts form a sequence, more specifically each amount is a term in an arithmetic sequence. To find the next term we just add $150.

6 What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, 8, 12, 16, 20………….. +4

7 What is the common difference? The difference between each number. This determines what is added to each previous number to obtain the next number. 4, 8, 12, 16, 20………….. 4 is the common difference

8 Geometric Sequence What if your pay check started at $100 a week and doubled every week. What would your salary be after four weeks?

9 GeometricSequence Starting $100. After one week - $200 After two weeks - $400 After three weeks - $800 After four weeks - $1600. These values form a geometric sequence.

10 What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. 3, 9, 27, 81, 243………….. x3

11 What is the common ratio? The number used to multiply by each previous number to obtain the next number. 2, 8, 32, 128, 512………….. 4 is the common ratio

12 Let’s Practice !

13 Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference

14 Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio

15 What is the next term in this sequence? 5, 20, 80, 320, _____ 1,280 x4 Is this an arithmetic or geometric sequence? What is the common ratio or difference?

16 What is the next term in this sequence? 5, -1, , _____ Is this an arithmetic or geometric sequence? What is the common ratio or difference?

17 What is the next term in this sequence? -3, 6, -12, 24, _____ -48 X-2 Is this an arithmetic or geometric sequence? What is the common ratio or difference?

18 What is the next term in this sequence? -400,-380,-360,-340, ____ Is this an arithmetic or geometric sequence? What is the common ratio or difference?

19 What is the next term in this sequence? 100, 75, 50, 25____ Is this an arithmetic or geometric sequence? What is the common ratio or difference?

20 What is the next term in this sequence? 12, -48, 192, -768____ 3,072 x-4 Is this an arithmetic or geometric sequence? What is the common ratio or difference?


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