Number Patterns and Rules

In short: To continue a number pattern, find how each term changes: by adding, subtracting, multiplying or dividing the same amount. If the jumps themselves change, look for a pattern in the jumps.

Before you start

• Times tables and adding.
• Powers: $2^3=2\times 2\times 2=8$ and $10^2=100$.
• Substituting a number into a rule like $y=2x+1$ (see Substitution in the Algebra unit).

Spotting the pattern

Look at how you get from one term to the next.

The rule for any term

If a pattern goes up by the same amount each time, the rule is

$$\text{term}=\text{jump}\times n+\text{something}$$

Rules with squares

A rule can use a square. Just substitute carefully.

Roman numerals

Some puzzles use Roman numerals.

Cross-number puzzles

In a cross-number puzzle, each row and each column follows the operation sign shown, such as $+$ or $\times$. Work out the boxes you know first, then use them to find the empty ones.

Quick summary

• Find how each term changes: add, subtract, multiply or divide.
• If the jumps change, write them down and look for a pattern in the jumps.
• A pattern that grows by the same jump has a rule like $3n+2$.
• Know the square numbers, cube numbers and doubling numbers.
• Roman numerals: I 1, V 5, X 10, L 50, C 100. A smaller one before a bigger one is taken away.

Quiz