What is a pattern?
A pattern is an arrangement of numbers, shapes or objects that follows a fixed rule. Once you spot the rule, you can continue the pattern or fill in missing parts. Patterns appear everywhere: tiles on a floor, days of the week, or the numbers 2, 4, 6, 8, ...
To find a rule, look at how each item changes into the next one. The change might be adding a fixed amount, subtracting, multiplying or dividing. Sometimes the rule uses squares (1, 4, 9, 16) or cubes (1, 8, 27).
Key idea / 要点
Compare each item with the one before it. A constant difference means you add or subtract; a constant ratio means you multiply or divide.
Finding the rule
Consider 3, 6, 12, 24, ... Each term is 2 × the term before it (6 ÷ 3 = 2, 12 ÷ 6 = 2). So the next term is 24 × 2 = 48.
Now look at 20, 17, 14, 11, ... Each term is 3 less than the one before, so the rule is "subtract 3" and the next term is 11 − 3 = 8.
Worked example / 例题
Find the next two terms of 1, 4, 9, 16, ...
These are square numbers: 12, 22, 32, 42. The next are 52 = 25 and 62 = 36.
Patterns with shapes
Dot and shape patterns can be counted and turned into number patterns. For triangular arrangements 1, 3, 6, 10, ... each new row adds one more dot than the row before (add 2, then 3, then 4). The next term is 10 + 5 = 15.
Remember / 记住
- Test your rule on every pair of terms, not just the first.
- Adding/subtracting gives a constant difference; multiplying/dividing gives a constant ratio.
- Watch for squares and cubes.