1. Patterns and Sequences

2. What is a Pattern ?
Things that are arranged following a rule or rules.
Example: these tiles are arranged in a pattern
Number Pattern:
A list of numbers that follow a certain sequence or pattern. Ex: there is a pattern in these numbers: 1, 4, 7, 10, 13, 16, …
The rule is "start at 1 and add 3 each time"

3. What is a Sequence?
A Sequence is a set of things (usually numbers) that are in order.
Each number in the sequence is called a term (or sometimes
"element" or "member"):
                                          

4. Patterns and sequences
For any pattern it is important to try to spot what is happening before you can predict the next number.
1, 2, 3, 4, 5, …
What comes next?

5. Patterns and sequences
Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.
5, 8, 12, 17, 23, 30, …
+ 5
+ 6
+ 7
+ 3
+ 3 X
+ 4

6. Finding Missing Numbers
To find a missing number or the next number you need to first find a Rule behind the Sequence.
Sometimes it is just a matter of looking at the numbers and seeing a pattern
Example: 1, 4, 9, 16, ?
Answer: they are Squares (12=1, 22=4, 32=9, 42=16, ...)
Rule: xn = n2
Sequence: 1, 4, 9, 16, 25, 36, 49, ...
In next slide let us see how to find the 25th term in this sequence

7. Example: Finding 25th Term
Remember the rule from last slide: xn = n2
Did you see how we wrote down that rule with "x" and "n" ?
xn means "term number n", so term 3 would be written x3
And we also used "n" in the formula, so the formula for term 3 is 32 = 9. This could be written x3 = 32 = 9
Once we have a Rule we can use it to find any term, for example, the 25th term can be found by "plugging in" 25 wherever n is.
x25 = 252 = 625

10. Patterns and sequences
Now try these patterns:
3, 7, 11, 15, 19, …, …
128, 64, 32, 16, 8, …, …
1000, , 10, 1, …, …
5, 15, 45, 135, …, …