9-1 Mathematical Patterns

Objectives

To identify mathematical patterns found in a sequence

To use a formula to find the nth term of a sequence

Image Long Description

Sometimes you can state a rule to describe a pattern. At other times, you have to do a bit of work to find a rule.

Essential Understanding If the numbers in a list follow a pattern, you may be able to relate each number in the list to its numerical position in the list with a rule.

A sequence is an ordered list of numbers. Each number in a sequence is a term of a sequence. You can represent a term of a sequence by using a variable with a subscript number to indicate its position in the sequence. For example, a 5 eh sub 5  is the fifth term in the sequence a 1 , a 2 , a 3 , a 4 , … . eh sub 1 , comma , eh sub 2 , comma , eh sub 3 , comma , eh sub 4 , comma dot dot dot .

The subscripts of sequence terms are often positive integers starting with 1.

If so, you can generalize a term as a n , eh sub n , comma  the nth term in the sequence.

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