Patterns And Relations Worksheet - Grade 7 Page 24
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46A Solution
Input
Output
Let any Input number be represented by n.
1
2
The input increases by 1 each time.
1
3
2
5
The output increases by 3 each time.
1
3
3
8
This means that the expression for the output
1
3
4
11
contains 3n.
1
3
5
14
Substitute several values of n in 3n, then
⎫
look for a pattern.
⎬
When n
1, 3n
3(1)
3
Each value is 1 more
When n
2, 3n
3(2)
6
than the output above.
⎭
When n
3, 3n
3(3)
9
That is, the output is
When n
4, 3n
3(4)
12
1 less than each value.
When n
5, 3n
3(5)
15
So, the output is 3n
1.
The table shows how 3n
1 relates to n.
Input
Output
Another Solution
1
2
3
1
1
Another way to solve this problem is to
2
5
3
2
1
notice that each output is 1 less than
3
8
3
3
1
a multiple of 3.
4
11
3
4
1
So, the output is 3
n
1, or 3n
1.
5
14
3
5
1
The table shows how 3n
1 relates to n.
n
n
3
1
Copy and complete each table.
1.
Explain how the Output number is related to the Input number.
a)
b)
c)
Input
Output
Input
Output
Input
Output
x
m
m
p
10
3p
5
2x
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
27
1.5 Patterns and Relationships in Tables
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