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
Find the next three numbers or terms in each pattern.
,...
22
,
17
,
12
,
7
a.
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.
22,...
17,
12,
7,
a.
5
5
5
,...
22
,
17
,
12
,
7
a.
The next three terms are:
27
5
22
32
5
27
37
5
32
37
,
32
,
27
5. Arithmetic Sequence
Find the next three numbers or terms in each pattern.
36,...
39,
42,
45,
b.
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.
36,...
39,
42,
45,
b.
)
3
(
)
3
(
)
3
(
The next three terms are:
33
)
3
(
36
30
)
3
(
33
27
)
3
(
30
36,...
39,
42,
45,
b.
27
,
30
,
33
6. Geometric Sequence
Find the next three numbers or terms in each pattern.
81,...
27,
9,
3,
b.
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 3 to each term.
81,...
27,
9,
3,
b.
3
3
3
The next three terms are:
243
3
81
729
3
243
1
2187
3
729
2
36,...
39,
42,
45,
b.
27
,
30
,
33
7. Geometric Sequence
Find the next three numbers or terms in each pattern.
64...
128,
256,
528,
b.
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 by 2 to each term.
64,...
128,
256,
528,
b.
2
1
or
2
2
1
or
2
2
1
or
2
The next three terms are:
32
2
64
2
1
1
64
32
2
64
or
16
2
32
2
1
1
32
16
2
32
or
8
2
16
2
1
1
16
8
2
16
or
64,...
128,
256,
528,
b.
8
,
16
,
32
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 ½.
8. Geometric Sequence
Find the next three expressions or terms in each pattern.
..
16
,
8
,
4
,
2
b. m
m
m
m
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 by 2 to each term or expression.
,...
16
,
8
,
4
,
2
b. m
m
m
m
2
2
2
The next three terms are:
m
m
32
2
16
m
m
128
2
64
m
m
64
2
32
,...
16
,
8
,
4
,
2
b. m
m
m
m
m
m
m 128
,
64
,
32
9. Arithmetic Sequence
Find the next three expressions or terms in each pattern.
..
11
8
,
8
6
,
5
4
,
2
2
b.
m
m
m
m
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 2m+3 to each term or expression.
,...
11
8
,
8
6
,
5
4
,
2
2
b.
m
m
m
m
3
2
m 3
2
m 3
2
m
The next three terms are:
15
10
3
2
11
8
m
m
m
21
14
3
2
18
12
m
m
m
18
12
3
2
15
10
m
m
m
,...
11
10
,
8
6
,
5
4
,
2
2
b.
m
m
m
m
21
14
,
18
12
,
15
10
m
m
m
