You are given a sequence of numbers: -2, 12, 32, 58, 90, ... Work out the 7th term in this sequence.

This is a question from Higher Tier and involves 1) realising that 2nd difference is a constant: 6. 2) knowing that constant 2nd difference implies the sequence is quadratic. 3) remembering or proving that constant of 2nd difference - "a" gives us the coefficient of n^2 in the sequence as (a/2)n^2. In our case the answer is (3)n^2. 4) Working out the whole sequence by calculating 3n^2 for n = 1, 2, ... 5 and subtracting the original sequence from the latter. 5) obtaining the linear sequence from the difference to be -5, 0, 5, 10, ... and calculating its (n)th term to be (5n - 10) for n > 0. 6) Merge the two (n)th term sequences into [3n^2 + 5n - 10]. 7) substitute 7 into the whole sequence to obtain 3*(7^2) + 5(7) - 10 = 172.