This document discusses patterns and sequences. It defines a pattern as a procedure or rule that can be followed to predict numbers in a sequence. An arithmetic sequence is one where the difference between consecutive terms is constant, while a geometric sequence is one where each term is formed by multiplying the previous term by the same number. Examples are provided of finding the next three terms in arithmetic and geometric sequences based on the pattern. It also notes that dividing a term is represented as multiplying by the reciprocal.

1. Patterns and Sequences
Henrico County Public School
Mathematics Teachers

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