TenMarks teaches you how to identify and apply arithmetic sequences.
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Learn about Arithmetic Sequences This lesson is about arithmetic sequences. The problem we’re going to use says; identify the pattern in the following sequence and then find the missing terms. So the sequence that’s given to us is 9, 19, 29, 39 and then two missing terms. What is a sequence? Let's first determine this. A sequence is an ordered set of numbers. Each of these numbers is called a term. This is a key to remember when the terms in a sequence changed by the same amount each time, we have an arithmetic sequence. Let me show you what I mean. I'm going to create a little bit of extra space. As we can see in this particular sequence, the terms are 9, 19, 29, 39 and we have to find the rest two. What is the difference between the first term and the second term? Well, the difference is I'm adding 10. Well if it is an arithmetic sequence, 10 should be the difference between the second and the third term as well. So 19 and 29 has a difference of 10. 29 to 39, there is a difference of 10. So we can see that we have a pattern. The first term, this is called the first term, it's nine. The second term is 19, third term is 29, fourth term is 39 and the difference between each term is 10. To get from one term to the next, I simply have to add 10. So now to find the missing terms, I simply have to add 10. So 39 + 10 = 49, so that will be the term here. To find the next one, I can add another 10. So 49 + 10 is 59, so I get 59 here. So the two missing terms are 49 and 59. That is the answer. Quickly recapping what we've learned; if we've got a sequence, it's an arithmetic sequence if the terms, each one of these sequence is called a term and the terms change by the same amount each time. It's an arithmetic sequence. In this case, I can see that the terms change by the same amount each time and that amount is 10. So using that, I can determine the last two or the missing terms in the sequence by adding 10 to 39 and by adding 10 to 49. The answer is 49 and 59.