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Home > Subjects > Mathematics > Level 1 > 1.3 Tables, equations and graphs (AS91028) > Subject content > Linear patterns

  • Subject: Mathematics
  • AS: 91028
  • Level: 1
  • Credits: 4
  • External

Mathematics 1.3 Investigate relationships between tables, equations and graphs

Linear patterns

In a sequence of numbers, each number is called a term.
For the sequence 2, 5, 8, 11, …
The first term is 2, the second term is 5, etc.

The gap between the numbers is called the difference.
In this example the difference is 3, because 5 – 2 = 8 – 5 = 11 - 8 = 3.

Linear patterns have the same difference between the terms.
To find the rule, look for a relationship between the number of the term and the term itself. The rule is the same for each term.
In this example: 2 = 3 x 1 – 1, 5 = 3 x 2 – 1 and 8 = 3 x 3 – 1,
so the rule is t = 3 x n – 1 or t = 3n - 1

Problem

For the sequence of diagrams below, find the rule for the number of white tiles (w) in terms of the number of black tiles (b).

algebraic diagram

Answer

Number of black tiles (b) Number of white tiles (w) Difference
1 8  
3 13 5
4 18 5
4    

The difference between each term is 5. (13 - 8 = 5, 18 - 13 = 5, etc)
The difference (5) is the multiplier, so the rule must be w = 5b + ?.
To work out the ?, substitute in b = 1 and w = 8 from the first line of the table
8 = 5 x 1 + ?.
The constant term must be 3.
Giving the rule as w = 5b + 3.

For more information see:
Constructing a formula
Finding the next number in a sequence
Recognising sequences
Sequences - Finding a Rule

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