Home > Subjects > Mathematics > Level 1 - CAS Mathematics > 1.1 Algebra (AS90799) > Subject content > Linear patterns
- Subject: Mathematics
- AS: 90799
- Level: 1
- Credits: 4
- External
CAS Mathematics 1.1 Demonstrate an understanding of straightforward algebraic methods
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).
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
To practice finding rules see: What is the rule for this sequence?
