Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 3

Which of the following sequences shows an arithmetic progression? Circle your answer. [A] 5, 8, 11, 14, ... [B] 2, 3, 5, 8, ... [C] 2, 4, 8, 16, ... [D] 3, 5, −3, −5, ...


Video Transcript

Which of the following sequences shows an arithmetic progression? Circle your answer. The options are: five, eight, 11, 14; two, three, five, eight; two, four, eight, 16; three, five, negative three, negative five.

Well, the first thing to ask is, what is an arithmetic progression? Well, an arithmetic progression is a sequence where there is a common difference between each of the terms. So what this means is that the difference between consecutive terms is constant. So for example, if you take a term away from the next term, the answer should be the same as if you took that next term away from the term afterwards, and so on.

So if we take a look at the first sequence, we’ve got five, eight, 11, and 14. Well, the difference between five and eight is three, cause you have to add three to get from five to eight. You have to add three to get from eight to 11. And then, again, you have to add three to get from 11 to 14. So therefore, this shows an arithmetic progression. Now, we’ve just circled this answer. But what I want to do is just double check that the other ones are not also arithmetic progressions.

Well, we can see that the next sequence on the top row is not an arithmetic progression. Because if you look at the differences, they increase. Because between two and three, you have to add one. Then to get from three to five, you add two. And then from five to eight, we add three. So this one would not be an arithmetic progression.

Now, let’s take a look at the sequence two, four, eight, 16. Well, again, this is not an arithmetic progression because the difference increases each time. So two to four is plus two. Four to eight is plus four. And then eight to 16 is plus eight. Some people might think, well, isn’t that a common difference, because you just multiply by two each time? But, that’s different. That’ll be a common ratio. So this would be a different type of sequence which is known as a geometric progression.

Then finally, the last sequence three, five, negative three, negative five is also not an arithmetic progression. And that’s because, as you can see, the difference changes each time. So you got plus two, minus eight, then minus two. So therefore, the only sequence that is an arithmetic progression is the first top-left one. And so, I’ve circled that. So five, eight, 11, 14 is an arithmetic progression because it has a common difference.

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