Predict next number from a series was closed recently, amid a number of comments to the effect that the next term could be anything, etc., etc.
Unlike other questions that have been discussed before (see, e.g., http://meta.math.stackexchange.com/questions/924/guess-the-next-number-guess-the-relation-etc), the question did not present a particular sequence and ask for the next number, but asked more generally for methods to determine the next number in a given sequence. This is a serious question. Sequences of numbers come up all the time, and we often have good reason to believe that there is some systematic rule behind them, and we do have methods for working out what the systematic rule might be. There are several pages about this topic in Chapter 2 of Sloane's A Handbook of Integer Sequences.
I have voted to reopen the question, so we can have a chance to have some of those methods posted in reply.