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**Patterns and Sequences**

Henrico County Public School Mathematics Teachers

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**Patterns and Sequences**

Patterns refer to usual types of procedures or rules that can be followed. Patterns are useful to predict what came before or what might come after a set a numbers that are arranged in a particular order. This arrangement of numbers is called a sequence. For example: 3,6,9,12 and 15 are numbers that form a pattern called a sequence. The numbers that are in the sequence are called terms.

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**Patterns and Sequences**

Arithmetic sequence (arithmetic progression) – a sequence of numbers in which the difference between any two consecutive numbers or expressions is the same Geometric sequence – a sequence of numbers in which each term is formed by multiplying the previous term by the same number or expression

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Arithmetic Sequence 1 Find the next three numbers or terms in each pattern. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add 5 to each term.

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**The Next Three Numbers Add five to the last term**

The next three terms are:

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Arithmetic Sequence 2 Find the next three numbers or terms in each pattern. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add the integer (-3) to each term.

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**The Next Three Numbers 2 Add the integer (-3) to each term**

The next three terms are:

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Geometric Sequence 1 Find the next three numbers or terms in each pattern. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to multiply each term by three.

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The Next Three 1 Multiply each term by three The next three terms are:

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Geometric Sequence 2 Find the next three numbers or terms in each pattern. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to divide each term by two.

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The Next Three 2 Divide each term by two The next three terms are:

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Note To divide by a number is the same as multiplying by its reciprocal. The pattern for a geometric sequence is represented as a multiplication pattern. For example: to divide by 2 is represented as the pattern multiply by a half.

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**Patterns & Sequences a) 7, 12, 17, 22, … b) 1, 4, 7, 10, …**

Decide the pattern for each and find the next three numbers. a) 7, 12, 17, 22, … b) 1, 4, 7, 10, … c) 2, 6, 18, 54, ... d) 20, 18, 16, 14, … e) 64, 32, 16, ... a) 27, 32, 37 b) 13, 16, 19 c) 162, 486, 1548 d) 12, 10, 8 e) 8, 4, 2

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