Arithmetic Progression/Sequence | Does it include terms prior to the initial term?

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I’m trying to find the right term to describe points along a linear equation f(x) = mx + b, but where the domain is restricted to the set of integers. EDIT: Also the slope and y-intercept are integers.

Off hand, an Arithmetic Progression/Sequence appears to fit the bill - except for the notion of an initial term. As the initial term, does that mean the sequence does not contain any terms prior to this along the same linear equation? Or am I overthinking it?