#EXAMPLES OF QUADRATIC SEQUENCES HOW TO#

Note that in this next one there is a NEGATIVE difference between the terms of the sequence on row 5. We can easily check this by adding up the seventh and eighth rows, which gives us the first row (the original sequence). It tells us to add -14 to 2n 2 + 4n, and that will be our solution: 2n 2 + 4n – 14. Finally we subtract (2n 2 + 4n) from our original sequence (subtract the 7th row from the first row): start First we calculate 4n, and then we calculate 2n 2 + 4n. So now we add some more rows to our grid. 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.

#EXAMPLES OF QUADRATIC SEQUENCES HOW TO#

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”.

Examples of quadratic sequences