The rule for the given pattern is multiply by four, then add one. What are the next two numbers? Three, 13, 53, what, and what. We have five possible pairs of answers, 211 and 843, 212 and 848, 212 and 849, 213 and 852, or 213 and 853.
This pattern has what we call a two-step rule. The reason we call it the two-step rule is because there are two things that we need to do to find each next number. In the question, we’re told what those two things are. First, we multiply by four, and then we add one. If we look underneath the arrow on the diagram, we can see an example of the first number.
First, we multiply by four, and then we add one. The first number in our pattern is three. So, we multiply this by four to get 12 and then add one to get 13. This is where our second number of 13 comes from. And the same two-step rule has been applied to find our third number. 13 times four is 52, and then if we add another one, it takes us to 53 too.
In order to find the next two missing numbers, we need to apply this two-step rule. And the number we need to start with is the number in the pattern that we get as far as, which is 53. So, let’s apply our rule. First thing we need to do is to multiply by four. Three times four equals 12. And five times four is 20. So, five tens times four is 20 tens. We’ve already got one 10 underneath, so this is 21 tens. 53 times four is 212.
And if we look at our missing answers, we can see that two of them have 212 as the first missing number. Could our answer be one of these? No, we’ve forgotten the second step of our two-step rule. We need to multiply by four, but then add one. And 212 plus one equals 213. The fourth number in our pattern then is 213. And we can see out of our possible answers that there are two that start with 213. One of these is going to be correct.
To find the final number in our pattern, we need to apply our two-step rule again. This time we’re going to start with 213. Three lots of four equals 12, which is two ones and one 10. One times four equals four. So, one 10 multiplied by four is four tens. We also got a 10 underneath, so that takes us to five tens. And two hundreds multiplied by four equals eight hundreds. 213 multiplied by four equals 852.
So, does that mean that this pair of numbers is correct? 213 and 852? No, we need to add one again. Instead of 852, our missing number is going to be one more than this, 853. We found the next two numbers in the pattern by starting with 53 and applying our two-step rule, which is to multiply by four and then add one. The next two numbers in the pattern after 53 are 213 and 853.