A quadratic sequence is a sequence where the nth term contains the term n2. While there is a 'correct' way of doing this, sometimes it is easier to see if the sequence is related to the sequence of square numbers (1, 4, 9, 16...),
The way we can check if this is the approach the examiner wants is to look how many marks it is worth, if it only carries 1/2 marks, use this apporach,
Example 1: Find the nth term of 2, 18, 18, 32...
Start by looking at the sequence 1, 4, 9, 16 (This has an nth term of n2)
You should notice that our sequence is double the square numbers. This makes our nth term 2n2
Example 2: Find the nth term of 3, 7, 11, 18...
Again, we can compare this with the square numbers and we notice that our sequence is just two more.
Our sequence would be n2 + 2
Example 3: Find the nth term of 19, 16, 11, 4
If we compare this to the square numbers, notice that they add up to 20.
This could be looked at as 'if I take the square numbers away from 20, I get my target'
This makes our nth term 20 - n2