 # Patterns and Sequences Patterns and Sequences Patterns refer

• Slides: 20 Patterns and Sequences 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– An arithmetic sequence is a set of numbers put into a specific order by a pattern of addition or subtraction. 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 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 terms are: Arithmetic Sequence 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 terms are: Geometric Sequence 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 3 to each term. The next three terms are: Geometric Sequence 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 by 2 to each term. 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 ½. Recursive Formula for Arithmetic Recursive formula is a formula that is used to determine the next term of a sequence using one or more of the preceding terms. The Sequence 2, 5, 8, 11, 14 …. Recursive Formula Recursive Formula Geometric The recursive formula for geometric sequences is different than the recursive formula for arithmetic sequences The Sequence 5, 25, 125, 625…. Recursive Formula Write the Recursive Formula for Arithmetic sequences Write the Recursive Formula for Geometric sequences Explicit Formula An explicit formula expresses the nth term of a sequence in terms of n. It can be used to find any term in the sequence based on the term number. Explicit formula for Arithmetic Write an Explicit formula for Arithmetic Write an Explicit formula for Arithmetic Finding the nth term in the Explicit formula for Arithmetic Explicit Formula for Geometric Write an Explicit formula for Geometric Write the Explicit formula for Geometric Finding the nth term in the Explicit formula for Geometric