Patterns &amp; Sequences

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# Patterns & Sequences - PowerPoint PPT Presentation

Patterns &amp; Sequences. Lesson 1. Define. Some people say that mathematics is the science of patterns. That\'s not a bad description. Not only do patterns take many forms over the range of school mathematics, they are also a unifying theme. Continued….

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### Patterns & Sequences

Lesson 1

Define
• Some people say that mathematics is the science of patterns.
• That\'s not a bad description.
• Not only do patterns take many forms over the range of school mathematics, they are also a unifying theme.
Continued…
• Number patterns—such as 3, 6, 9, 12—arefamiliar to us since they are among the patterns we first learn as young students.
• How can you tell if a number sequence is a pattern?
• Anumber sequence is a pattern if the sequence follows a specific rule.
Is it a pattern? Why or Why Not?

19, 28, 37, 46, 55, …

63, 58, 53, 48, 43, …

-2, -4, -6, -8, -10, …

-7, 45, 89, 15, -36, …

32, 36, 41, 47, 54, …

4, 8, 11, 22, 25, 50, 53, …

Yes, subtract 5

Yes, subtract 2

No

Yes, +4, +5, +6, +7…

Yes, •2, +3, •2, +3, •2, +3, …

Is it a pattern? Why or Why Not?

1.

2.

3.

4.

Yes, subtract 4

Yes, multiply by ½

Yes, multiply by 2

Types of Patterns
• Iterative Pattern
• Follows a rule
• Can be represented as an input/output model
• For example: 4, 8, 12, 16… is an Iterative pattern because it follows the rule “add 4.”
• Recursive Pattern
• Is defined by the previous term
• For example: 1, 1, 2, 3, 5, 8, 13… is a recursive pattern because to get the next term you have to add the two previous terms together.
• 19, 28, 37, 46, 55, …
• 63, 58, 53, 48, 43, …
• -2, -4, -6, -8, -10, …
• -7, 45, 89, 15, -36, …
• 32, 36, 41, 47, 54, …
• 4, 8, 11, 22, 25, 50, 53, …

Iterative. You subtract 5.

Iterative. You subtract 2.

Not a pattern.

Recursive. You add 4, then add 5 to the previous term then add 6 to the previous term.

Recursive. You multiply the previous term by 2 then the next term you add 3.

1.

2.

3.

4.

Recursive. You double the previous number and subtract 5.