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. $2550 + 2652=5202.$ $51$ squared then times $2$ equals $5202.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”. The result equals the middle number squared, then times by $2$. Rubayat, Hondfa, Jacob and Nathan represented the problem numerically and in words: $(n-1)(n+1)= n^2-1$, so $(n-1)(n+1)+1=n^2$Ĭhloe, Sophia and Shreya from North London Collegiate School made a clear diagram with a good explanation:
Peter's proof was different to Charlie's: The pattern is what Charlie quoted,"If you multiply two numbers that differ by 2, and then add one, the answer is always the square of the number between them!" $3 \times 5 + 1= 16$ or $4^2$. Rubayat, Hondfa, Jacob and Nathan from Greenacre Public School in Australia noticed that Maddy and Grace from the Stephen Perse Foundation in the UK continued the numerical pattern: The shaded area in the right hand diagram needs to be 'subtracted' from the green area. "If you choose four consecutive numbers and subtract from the product of the two middle ones the product of the other two, then you always get $2$." Peter from Durham Johnson School in the UK noticed that the expressions all simplify to 2: Tiago and Finn's diagram representation looked like this: Marc and Yang called the numbers $x$ and $y$ and noticed thatĪmrit's proof used Marc and Yang's idea to prove Peter's representation in words. The answer is always the sum of the digits.
If you multiply the two consecutive numbers, which differ by one, then add the bigger number to that you're always going to get the square of the bigger number. Viktor and Matija spotted a numerical pattern and summarised it in words: Amrit from Hymers College in the UK, Radi and Camilla and Viktor and Matija from European School Varese in Italy, Rubayat, Hondfa, Jacob and Nathan from Greenacre Public School in Australia, Ryan from Dulwich College Seoul in Korea and Peter from Durham Johnson School in the UK sent in good work on this problem.
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