![]() Note also that in the case of a linear sequence, we do NOT divide the number by 2. Note that this is because we have found a linear sequence. This tells us that there will be a 4n in our answer. We need to look at the gaps between the numbers in our new sequence (in the bottom row of the table): We don’t have a row of constant numbers yet, so we need to keep working. So in the below grid, we subtract the fourth row from the first row, and that gives us a new sequence, which we have placed in the fifth row: start Now, subtract 2n 2 from the original sequence. Below that, add whatever rows you need to help you calculate 2n 2. This tells you that your final result will contain the term 2n 2.Ĭreate a grid, which starts with your original sequence. Take that 4 and divide it by 2 (it’s easy to forget to divide by 2!), to get 2. Then find the gaps between the gaps – these are 4 and 4. Most Complex Example ( an 2 + bn + c):įind the nth term for the following quadratic sequence: -8, 2, 16, 34, …įirst calculate the gaps between the numbers – these are 10, 14 and 18. We can easily check this by adding up the fourth and fifth rows, which gives us the first row (the original sequence). ![]() It tells us to add -2 to 3n 2, and that will be our solution: 3n 2 – 2. Now, subtract 3n 2 from the original sequence. Below that, add whatever rows you need to help you calculate 3n 2. More Complex Example ( an 2 + b):įind the nth term for the following quadratic sequence: 1, 10, 25, 46, …Ĭreate a grid, which starts with your original sequence. But you should always check your results: n I’ve already told you that this is a simple example – we’ve reached our solution: 3n 2. This tells you that your final result will contain the term 3n 2. Take that 6 and divide it by 2 (it’s easy to forget to divide by 2!), to get 3. Then find the gaps between the gaps – these are 6 and 6. Simplest Example ( an 2):įind the nth term for the following quadratic sequence: 3, 12, 27, 48, …įirst calculate the gaps between the numbers – these are 9, 15 and 21. You’re aiming for a result of an 2 + bn + c, but easier examples might have a solution of an 2 + b, and even easier ones will just be an 2. So I’m placing my notes here in case they’re any use to anyone else. I couldn’t find decent complex examples on either of my favourite GCSE maths revision sites ( Maths Genie and BBC Bitesize), and when you’re doing the more complex examples, a step-by-step guide is really useful. I’m an ex high school maths teacher, but I had forgotten how to do this. I’m currently helping my 15-yr-old son revise for his maths GCSE, and one topic is “finding the nth term of a quadratic sequence”.
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