I don't know if I'm in the right sub-forum here, but I've seen questions about sequences and series here before, so here we go.

Our teacher gave us a brainteaser by giving us the first nine numbers in a sequence and then challenging us to find the expression for

. The problem is that it's not very easy, and I'm not sure if I'm going to be able to solve it with my current set of skills. So my question is: Are there methods to find a possible sequence if given certain information, and if so, what are they and how advanced are they? What do I need to know in order to use them?

And btw, if you want to have a crack at the brainteaser I can post the first nine numbers, but I really wish to solve this one myself, so please don't post any spoilers in case that you solve it before I do.