What is the missing number in this pattern? 108, 87, what, 45, 24.
Here, we’ve got a pattern of five different numbers although, unfortunately, we can only see four of them. We’ve got a missing number in the center. And the question asks us, what is this missing number? We need to use the information around the missing number, that’s the other numbers in the sequence, to help us. Now, when we have a pattern like this, it’s often useful to have two numbers that are next to each other. This can really help us to find out what the rule is for the pattern. Well, interestingly, in this particular pattern, we have two pairs of numbers that are next to each other. And so, if we look at how we get from 108 to 87. And also, to check our rule, we could see how we get from 45 to 24. We could use the rule that we find to find out what our missing number is.
The first thing that we can say about our pattern is that it’s a decreasing pattern. The numbers are getting smaller from left to right. We start with 108 and we end up with 24. And each time, the number gets smaller. So it looks like the rule might be a subtraction rule. We might be taking away a certain amount each time. Let’s begin by looking at our first pair of numbers then to try and work out what this rule is for the pattern.
How do we get from 108 to 87? What do we subtract? Well, we can get quite close to 87 by simply subtracting 20. 108 take away 20 or two 10s takes us to 88. And then to get from 88 to 87 is a small jump of one. So altogether, we’ve subtracted 20 and one. That’s 21. Now, although it looks like our rule might be to subtract 21 each time, if we can check it, it’s always a good idea to. And, in this case, we can check it. We can look at the last pair of numbers, 45 and 24. 45 contains four 10s and five ones. Now, remember, we want to test whether the rule is to subtract 21 each time. 21 is made up of two 10s and one one. So let’s subtract two 10s from our four 10s. And we’ll also subtract one one from our five ones. What are we left with if we take away 21 from 45?
We can see that we have two 10s and four ones, 24. And if we look at our pattern, we can see this is the number we expected. The rule is: take away 21 each time. So the final step is to apply our subtract-21 rule by taking away 21 from 87 to find the missing number. 87 is made up of eight 10s and seven ones. And remember, we’ve said that the number we need to take away, which is 21, is made up of two 10s and one one. Eight 10s take away two 10s leaves us with six 10s. Now, let’s take away our one one that we need to subtract. Seven ones take away one one leaves us with six ones. Six 10s and six ones. The rule for our pattern was to subtract 21 each time. And the missing number in the pattern is 66.