Number Patterns & Rules

The first thing to do with any pattern is find the gap between each pair of numbers, and write those gaps above the pattern. Two, four, six, eight — every gap is plus two. So the rule is add two, and the next number is ten. Writing the gaps down takes a few seconds and it turns a pattern question into an easy one, so do it every time rather than staring at the numbers hoping to see it.

A pattern that goes down works exactly the same way, and only the sign changes. Forty, thirty-six, thirty-two, twenty-eight — every gap is take away four, so the rule is subtract four and the next number is twenty-four. The test will offer thirty-two as a wrong answer, because that is what you get going the wrong way. So check which direction the numbers are travelling before you pick.

Some patterns multiply instead of adding. One, two, four, eight, sixteen — the gaps are plus one, plus two, plus four, plus eight, all different, so it is not an adding pattern. But each number is double the one before, so the rule is multiply by two and the next number is thirty-two. If the gaps are not the same, that is the second thing to try: is each number double the one before, or triple? Multiplying patterns grow fast, so the numbers get big quickly.

Here is the hardest pattern type on the paper. Ten, eleven, thirteen, sixteen, twenty, twenty-five. The gaps are plus one, plus two, plus three, plus four, plus five — they go up by one each time. This is not doubling; the numbers grow slowly, and it is the gap that grows. So the next gap is plus six, and twenty-five plus six is thirty-one. When the gaps are not all the same, look at the gaps between the gaps. Writing them down is what solves this question.

Three questions, in this order. One: are all the gaps the same? If they are, the rule is add or take away that number. Two: is each number double the one before? If it is, the rule is multiply by two. Three: are the gaps growing by the same amount? If they are, work out the next gap and add it on. Work down that list and you will find every pattern on the paper. Then check by running your rule from the very first number. Quiz and exercises now.