First, please take a look at http://www.purplemath.com/modules/nextnumb.htm (the second-order sequence problem) http://www.purplemath.com/modules/nextnumb.htm : "Since these values, the "second differences", are all the same value, then I can stop. It isn't important what the second difference is (in this case, "2"); what is important is that the second differences are the same, because this tells me that the polynomial for this sequence of values is a quadratic.(Once you've studied calculus, you'll be able to understand why this is so. For now, just trust me that this works.)" And now, I've studied introductory (basic differentiation and integration) But, I still have no idea what calculus for sequence is. Please explain me or give me a link to a web which clearly explains it.