Recursive and explicit rules
A sequence can be defined recursively, with each term built from the one before it, like f(n) = f(n-1) + 3, or explicitly, with each term computed directly from its position, like f(n) = 3n + 2; for example, f(1) = 3(1) + 2 = 5, and the recursive rule agrees: f(2) = f(1) + 3 = 5 + 3 = 8, matching 3(2) + 2 = 8. Arithmetic sequences (constant difference) can be written either way, just as geometric sequences (constant ratio) can for exponential functions.
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