FORMULAS FOR SEQUENCES Is there any easy way to find an explicit formula for a(n), the nth term of a sequence, when the first few terms are given without having to guess and look for patterns?
I think it’s safe to say that you must look for patterns! It helps me to first look for a recursion formula by seeing if there is a pattern to the way that each term in the sequence is related to its immediate predecessor. If I can get a recursion formula, then I can often easily get an explicit formula in terms of some function of n.
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