2. 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.
3. 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
4. Arithmetic Sequence 1
Find the next three numbers or terms in each pattern.
5
5
5
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.
5. The Next Three Numbers
Add five to the last term
The next three terms are:
6. Arithmetic Sequence 2
Find the next three numbers or terms in each pattern.
)
3
(
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.
)
3
(
)
3
(
7. The Next Three Numbers 2
Add the integer (-3) to each term
The next three terms are:
8. Geometric Sequence 1
Find the next three numbers or terms in each pattern.
3
3
3
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 each term by three.
9. The Next Three 1
Multiply each term by three
The next three terms are:
10. Geometric Sequence 2
Find the next three numbers or terms in each pattern.
2
1
or
2
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 each term by two.
2
1
or
2
2
1
or
2
11. The Next Three 2
Divide each term by two
The next three terms are:
12. 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 a half.
13. Patterns & Sequences
Decide the pattern for each and find the next three numbers.
a) 7, 12, 17, 22, …
b) 1, 4, 7, 10, …
c) 2, 6, 18, 54, ...
d) 20, 18, 16, 14, …
e) 64, 32, 16, ...
a) 27, 32, 37
b) 13, 16, 19
c) 162, 486, 1548
d) 12, 10, 8
e) 8, 4, 2
