Patterns and Rules
Spotting how a sequence grows to predict later terms.
Key idea
Spotting how a sequence grows to predict later terms.
In depth
A pattern is a repeating or predictable structure. To find a rule, look at differences or ratios between terms, express the nth term as a formula, and test it against known terms. A rule must work for all terms, not just the ones you see.
Worked example
1, 4, 9, 16, ... has differences 3, 5, 7, so the rule is n².
Real-world uses
- Predicting the next figure in an IQ test
- Spotting trends in sales data over the months
Common mistake
Deciding on a rule from only two or three terms.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Patterns and Rules?
Spotting how a sequence grows to predict later terms. It is a topic at the beginner level in Arithmetic & Number Sense.
Where is Patterns and Rules used in real life?
Real-world examples: Predicting the next figure in an IQ test; Spotting trends in sales data over the months.
What should I learn before Patterns and Rules?
Make sure you are comfortable with Geometric Sequences (Intro), the previous topic in Arithmetic & Number Sense.
What is a common mistake with Patterns and Rules?
Deciding on a rule from only two or three terms.
How can I practise Patterns and Rules?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Patterns and Rules?
Move on to Fibonacci Numbers next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Place Value – The value of a digit depends on its position: ones, tens, hundreds and so on.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.