Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Classify a sequence as arithmetic, geometric, both, or neither
Problem
Classify the sequence \(4,~7,~10,~13\) as arithmetic, geometric, both, or neither, and justify the classification.
Big Picture
What this problem is really about
Sequence classification requires testing definitions rather than judging whether the list merely looks regular. We’ll compute every consecutive difference for the arithmetic test and every consecutive ratio for the geometric test, then compare the consistency of each set. The classification follows from exactly which tests hold, with the numerical evidence providing the justification.
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