Download Patterns and Sequences

Patterns and Sequences
Henrico County Public School
Mathematics Teachers
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.
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
Arithmetic Sequence 1
Find the next three numbers or terms in each pattern.
7, 12, 17, 22,...
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.
The Next Three Numbers
7, 12, 17, 22...
Add five to the last term
The next three terms are:
27, 32, 37.
22 5 27
27 5 32
325 37
Arithmetic Sequence 2
Find the next three numbers or terms in each pattern.
45, 42, 39, 36...
45, 42, 39, 36...
 (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 add the integer (-3) to each term.
The Next Three Numbers 2
45, 42, 39, 36...
Add the integer (-3) to each term
The next three terms are:
33,
30, 27.
36  (3)  33
33 (3)  30
30  (3)  27
Geometric Sequence 1
Find the next three numbers or terms in each pattern.
3, 9, 27, 81...
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.
The Next Three 1
3, 9, 27, 81...
Multiply each term by three
The next three terms are: 243,
81
 3
243
243
3
729
729, 2187
729
3
2187
Geometric Sequence 2
Find the next three numbers or terms in each pattern.
528, 256, 128, 64...
528, 256, 128, 64...
 2 or 
1
2
 2 or 
1
2
 2 or 
1
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.
The Next Three 2
528, 256, 128, 64...
Divide each term by two
The next three terms are:
64  2  32
or
64  1  64  32
1 2 2
32, 16, 8.
32  2 16
or
32  1  32 16
1 2 2
16  2  8
or
16  1  16  8
1 2 2
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.
16  2  8
is the same as
16  1  16  8
1 2 2
Patterns & Sequences
Decide the pattern for each and find the next three numbers.
a) 7, 12, 17, 22, …
a) 27, 32, 37
b) 1, 4, 7, 10, …
b) 13, 16, 19
c) 2, 6, 18, 54, ...
c) 162, 486, 1548
d) 20, 18, 16, 14, …
d) 12, 10, 8
e) 64, 32, 16, ...
e) 8, 4, 2