Write the next two terms in the following sequence: three, five, nine, 17, what, what.
So here we have a number sequence that starts three, five, nine, 17, and so on. And we need to find the next two values. The word terms is simply how we describe the values or the numbers in our sequence. So let’s see if we can find a pattern in the sequence that will allow us to find the missing terms. A good way to start when we’re trying to find missing terms is to see if there’s a common difference between the terms in our sequence. So let’s see what we would add or subtract to our first term, three, to get to our second term, five.
Well, we could simply add two. And now, let’s look at seeing how we go from our second term, five, to our third term, nine. In this case, we could add four. And then, to go from our third term, nine, to our fourth term, 17, we could simply add eight. At this point, though, it might not seem particularly clear how we go from 17 to the next two terms. If we’d had, for example, the difference being plus two each time, then we could simply add on another two to get to 17. And that would give us the answer, but that’s not true here. So let’s have a closer look on our differences and see if we can find a pattern there.
Here, we can see that the differences double each time. So to find our next difference, we would simply double our plus eight, giving us plus 16 and meaning that the difference between our fourth term, 17, and the fifth term must be 16. And so, since 17 plus 16 gives us 33, then our missing fifth term is 33.
So to find our missing sixth term, we need to work out the difference between it and the fifth term, 33. As we know that our differences are doubling every time, if our last difference was 16, then our next difference will be equal to 16 times two, giving us a difference of 32. And so, our sixth missing term will be equal to 33 plus 32, which gives us 65. This means that our answer for the next two terms in the sequence is 33 and 65.