Find the nth term in the sequence
-6,-3,0,3,6

First, determine what type of sequence the set of numbers make up. Through simple logic, it is an arithmetic sequence, because one can see by inspection that there is a common difference of 3 (positive 3, just to be a bit more pedantic).

We then use the formula, 
where  represents the  term; a represents the starting term (so the first number in the set of numbers, which in this case is -6); n is the term number (1st, 2nd, 3rd term, etc.); d is the common difference, that is, when you subtract the next term to the previous term – what is that numerical value.

To elaborate a bit more, your 1st term is -6, 2nd is -3, 3rd is 0, etc.

Also, the formula above is something you just learn, unless you learn to proof this formula, which is something different.

So, here, , which can be expanded to:

Therefore,