Sequences - Arith v Geo

Sequences

- Arithmetic v Geometric

By Amy Latsch

A sequence is

​any list of numbers that is created by following a pattern

​Ex: 1, 3, 5, 7, 9,....

Ex: 2, 4, 8, 16, 32,...

Ex: 100, 90, 80, 70,...

Ex: 625, 125, 25, 5,...​

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TERM - a number in a sequence

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Multiple Choice

What is the second TERM in the sequence:

1, 3, 5, 7, 9, ....

• 1

• 3

• 5

• 7

Multiple Choice

What is the first TERM in the sequence:

81, 27, 9, 3 ....

• 3

• 9

• 27

• 81

Open Ended

What is the rule needed to continue the pattern?

5, 10, 15, 20, 25,....

​When you repeatedly MULTIPLY/DIVIDE BY a number to get the next number

​

The # you use is the COMMON RATIO

When you repeatedly ADD/SUBTRACT a number to get the next number

​

The # you use is the COMMON DIFFERENCE​

​Arithmetic v Geometric

There are 2 types of sequences

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Multiple Choice

Is the following arithmetic or geometric?

128, 64, 32, 16, 8,....

• arithmetic

• geometric

Multiple Choice

Is the following arithmetic or geometric?

5, 10, 15, 20, 25,....

• arithmetic

• geometric

​Ratio

Subtract second - first

third - second

fourth - third

Etc. If all are the same...that's the common difference​

​Difference

To find the COMMON

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Divide. second/first

third/second fourth/third

Etc. If all are the same...that's the common difference​

Multiple Choice

What is the COMMON DIFFERENCE?

5, 10, 15, 20, 25,....

• -5

• +5

• x2

• x1/2

Multiple Choice

What is the common ratio?

128, 64, 32, 16, 8,....

• -64

• + 64

• x 2

• x 0.5

Multiple Choice

Arithmetic sequences involve

• multiplication and division
• multiplication and addition
• addition and subtraction
• subtraction and division

Multiple Choice

Geometric sequences involve

• multiplication and division
• multiplication and addition
• addition and subtraction
• subtraction and division

Multiple Choice

Is the sequence geometric or arithmetic?
3, 6, 9, 12...

• Arithmetic
• Geometric
• Neither

Multiple Choice

Is the sequence geometric or arithmetic?
6, 18, 54...

• Arithmetic
• Geometric
• Neither

Multiple Choice

Is this arithmetic, geometric or neither. 
30,39,48,57,66,...

• Arithmetic
• Geometric
• Neither
• There's a difference???

Multiple Choice

Identify the common difference. 
10, 20, 30, 40, ...

• 5
• 10
• 15
• 20

Multiple Choice

Identify the common difference.
97, 86, 75, 64, ...

• 8
• 11
• -11
• -8

Multiple Choice

What are the next 3 terms in this sequence of terms? 3, 7, 11, 15

• 18, 22, 26
• 19, 21, 23
• 19, 23, 27
• 18, 21, 24

Multiple Choice

The next term of the sequence 4,16,64 is

• 256
• 132
• 120
• 150

Multiple Choice

What is the common ratio for the sequence:
28, 14, 7, 3.5...

• 2
• 1/2
• -14
• -7