How to find the nth term of a quadratic sequence?

Find the difference between each term in the sequence. Then find the second difference, i.e. the difference between each of the primary differences. Divide this by 2, to give you the coefficient of n^2. Now rewrite your sequence and below each term, the respective 'coefficient n^2'. Subtract one from the other, which will leave you with a linear sequence. By GCSE level, student should know how to calculate the nth term of a linear sequence, but if not then will run through how to do this.