Patterns and Sequences Henrico County Public School Mathematics

Patterns and Sequences Henrico County Public School Mathematics Teachers

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.

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

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.

The Next Three Numbers Add five to the last term The next three terms are:

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.

The Next Three Numbers 2 Add the integer (-3) to each term The next three terms are:

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.

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

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.

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

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.

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