What is the next number in this pattern? Three, six, 12, 24, what?
We’re given four numbers. And we’re told that they make a pattern. We can see that the fifth circle is blank. We need to find the next number in the pattern, the fifth number. Now, this problem teaches us a valuable lesson in identifying patterns. Sometimes we can look at perhaps two numbers and think that we know what the pattern is.
For example, we might look at the first two numbers and think three, six. Oh, we can see what the pattern is. It’s the three times table. We’re just adding another lot of three every time. And so, we might try to answer the question quickly, whizz along to the end of the pattern, and see that we have the number 24, and then just add three to it to give us an answer of 27. But we haven’t looked at the other numbers in the pattern. We’ve simply looked at the first two numbers and thought that we knew what the pattern was.
It’s always important to look at more than two numbers. And as we’ll go on to see now, the answer isn’t 27. So, let’s start again. And this time, we’ll look at all the numbers in the pattern. Now, as we’ve said already, to get from three to six, we add three. But there’s another way to get from three to six. And that’s to multiply by two. Three times two equals six.
Now, let’s look at the next two numbers in the sequence. How do we get from six to 12? Well, firstly, we can see an addition rule, but it’s not plus three this time. It’s plus six. If we have six and we add six, this is the same as multiplying by two. So, we can see where both these rules come from. Now, let’s look at the third and fourth numbers, 12 and 24. Again, we can see that we can add another lot of 12. So, 12 plus 12 equals 24. Or we know this is the same as multiplying by two.
So, we seem to have found two rules. The first rule we could describe as add itself. So, if we start with three, we then add another lot of three. That gives us six. We then add another lot of six, which gives us 12. We then add another lot of 12, and so on. The problem with this rule is that the number we add each time changes. It’s not a rule that we can say stays the same. So, perhaps it’s better to think of the rule as a multiplication because adding itself every time is simply doubling anyway.
If we multiply each number by two, then we get the next number in the sequence. So, our fourth number is 24. We now know how we can find the next number in the pattern. We can either choose to add itself. So, we find 24 plus 24. Or we multiply it by two. Both methods will give us exactly the same answer. Four plus four equals eight. And 20 plus 20 equals 40. Four times two equals eight. And two 10s times two equals four 10s. We found that the pattern showed a doubling rule, three, six, 12, 24. And the next number in the pattern is 48.