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Representing Patterns
Name:_____________________
Terminology
Linear patterns: a sequence of numbers in which the pattern only involves addition or subtraction.
Common Difference d : is the difference between any two consecutive numbers in a linear pattern.
Example 1: Determine the common difference of the following linear patterns and use it to find the next 3
numbers.
a) 4, 7, 10, 13,_______,________,________
b) -4, 0, 4, 8,______,_______,_______
c) -4, -10, -16, -22,________,________,________
d) 20, 15, 10, 5, ______,_______,_______
Representing a linear pattern:
Example 2: A pattern 5, 7, 9, 11,… can be rewritten in a chart called a table of values
Position ( x )
1
2
3
4
Pattern Number ( y )
5
7
9
11
2
2
y  2(1) + ? = 5
y  2(2) + ? = 7
y  2(3) + ? = 9
2+?=5
4+?=7
6+?=9
?=3
y  2x  3
2
Because the pattern goes up by 2 each time, the pattern can be represented by the linear relation y  2 x  ?
where x is the position of the pattern number y .
Knowing that the pattern number can be found by using the relation y  2 x  3 , we can now find the
number in the 12th position ….. y  2(12) + 3 which is y  27. This means that the 12th number in the
pattern is 27.
Example 3: Now try these rewrite the pattern using a table of values and determine the equation to
represent the relation:
a) 6, 10, 14, 18 …
b) 9, 11, 13, 15….
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Representing Patterns
Name:_____________________
c) 2, 5, 8, 11…
d) -1, 4, 9, 14 …
e) 1, -1, -3, -5 …
f) 3, 2, 1, 0 ….
Example 4: Write an equation relating C to n. (Verify it works for every pair of values)
a)
n
1
2
3
4
C
5
8
11
14
b)
n
1
2
3
4
C 3
2
7
12
2
c)
n
1
2
3
4
C
0
6
12
18
Representing Patterns
Name:_____________________
Example 5: Determine the 30th number in the following linear patterns.
a) 3, 8, 13, 18, …
b) -1, 2, 5, 8, …
c) 2, 6, 10, 14, …
d) 10, 7, 4, 1, ...
Example 6: If the following pattern of figures continues, determine the number of squares in the 10th
figure?
a)
b)
Figure 1
Figure 2
Figure 3
Fig 1 Fig 2
Fig 3
Fig 4
Example 7: In the following patterns, determine the number of sides needed to produce 20 polygons.
a)
b)
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Representing Patterns
Name:_____________________
Example 8: A banquet table seats 8 people, three on each side and one on
each end as shown in the diagram. Tables can be connected end to end.
a) How many additional people can be seated when a table is added?
b) Make a table to show how many people can sit at 1, 2, 3 & 4 tables.
c) Find a pattern and write an equation. Use n for the number of tables and P for the number of people.
d) Use your equation to determine how many people can be seated at 10 tables.
e) How many tables are needed to seat 344 people?
Example 9: Write an equation to represent the number of circles in relation to the figure number.
Figure 1
Figure 2
Figure 3
Figure 4
a) How many circles are in Figure 71?
b) Which figure number has 83 circles?
Example 10: The fare for a taxi ride is $1.50 per kilometre plus a fixed cost of $2.40.
a) Write an equation for the fare F in terms of the fixed cost and the cost per n kilometres.
b) What is the fare for an 11km ride?
b) If you cost was $32.40, how many km was the ride?
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