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 (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 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:

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:

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. 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. The next three terms are:

Geometric Sequence Find the common ratio for the following geometric sequences.

Geometric Sequence Do you see a pattern? To determine the general formula for the nth term of a geometric sequence, we should examine the following sequence: Do you see a pattern?

Geometric Sequence The general formula for the nth term of a geometric sequence is: The number of the term The common ratio The nth term Term 1

Geometric Sequence Name the nth term and determine t12 for each of the following geometric sequences.

“But these two ratios must be equal!” Geometric Sequence k-1, 2k, 21-k are three consecutive terms of a geometric sequence. Find k. k-1 2k 21-k “But these two ratios must be equal!” = Product =105 #’s are - 15 & - 7 Sum = -22

Geometric Sequence A geometric sequence has t2 = - 6 and t5 = 162. Find its general term. 1 2