Numeric and Geometric Patterns

A pattern is a sequence of numbers or shapes that follows a rule. To extend it, find what stays the same from one term to the next.

• Constant difference (adding): $3, 7, 11, 15, \ldots$ — each term is $4$ more than the one before, so the next is $19$.
• Constant ratio (multiplying): $2, 4, 8, 16, \ldots$ — each term is $\times 2$ of the previous, so the next is $32$.

Geometric patterns are the same idea drawn with shapes — for example matchstick figures that grow by a fixed number of matches each step.

Worked example. Continue $5, 11, 17, 23, \ldots$. The difference is $6$ each time, so the next term is $23 + 6 = 29$.

Exam checkpoint

Patterns are not guesses: they have a repeated change or a repeated multiplication. Write at least three terms, calculate consecutive differences, and check whether they stay constant. If they do, the pattern is linear. For a geometric pattern, compare by division instead.

Short worked example. For $5,8,11,14,\ldots$, each term increases by 3, so the next two are 17 and 20. The rule is ‘start at 5, add 3 each time.’