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**Arithmetic and Geometric Sequences**

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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.

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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.

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**Arithmetic Sequences Monday : $150 Tuesday: $300 Wednesday: $450**

Thursday: $600 Friday: $750

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Arithmetic Sequences 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.

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**What is an arithmetic sequence?**

A sequence in which each term is found by ADDING the same number to the previous term. 4, 8, , 16, 20………….. +4 +4 +4 +4

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**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

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

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**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.

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**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, , 81, ………….. x3 x3 x3 x3

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**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

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Let’s Practice!

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**Is this an arithmetic or geometric sequence?**

10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference

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**Is this an arithmetic or geometric sequence?**

2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio

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**What is the next term in this sequence? 5, 20, 80, 320 , _____**

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

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**What is the next term in this sequence? 5, -1, -7 -13 , _____**

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? 5, -1, , _____ -6 -6 -6 -6 -19

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**What is the next term in this sequence? -3, 6, -12, 24 , _____**

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

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**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? What is the next term in this sequence? -400,-380,-360,-340 , ____ +20 +20 +20 +20 -320

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**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? What is the next term in this sequence? , 75, 50 , 25____ -25 -25 -25 -25

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**What is the next term in this sequence? 12, -48, 192 , -768____**

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

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