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Patterning
A pattern is a group of numbers, shapes, or objects that follow a rule while
repeating or changing. To extend a pattern you can use a table or a pattern rule that relates the term
number to the pattern rule.
A term number
A number that tells the position of a term in a pattern.
1, 3, 5, 7, …
5 is the 3rd term
or term number 3
A pattern rule to get any number in the pattern is multiply 2 by the term
number.
10th term = 2 x 10
= 20
A recursive pattern rule is a pattern rule that tells you the start
number of a pattern and how the pattern continues.
For example, a recursive rule for the pattern 5, 8, 11, 14, … is
The pattern begins with 5 and you add 3 each time.
A common difference is the difference between any two consecutive terms in a pattern.
Not all patterns have a common difference.
For example, the pattern 5, 10, 15, 20, … has a common difference of 5.
The pattern 1, 4, 9, 16, … has no common difference.
An explicit pattern rule is a pattern rule that tells you how to get any term in
the pattern without listing all the terms before it. Any term = first term +[(term number - 1)] x (common difference)]
For example, an explicit pattern rule for 5, 8, 11, 14, … uses the first term (5) and the common difference (3).
To calculate the 20th term,
20th term = first term +[(term number - 1)] x (common difference)]
= 5 + [(20-1) x 3]
= 5 + [19 x 3]
= 5 + [57]
= 62
The 20th term would be 62.
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