Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Model an arithmetic situation with explicit and recursive rules
Problem
Row \(1\) has \(12~\text{seats}\), and each next row has \(4~\text{more}~\text{seats}\). Write both the explicit and recursive arithmetic-sequence rules.
Big Picture
What this problem is really about
The context describes a discrete sequence with a starting row and a constant additive change. We’ll define the indexed seat count, translate the first row and per-row increase, and express the same structure once by counting all transitions and once by updating from the previous row. Checking one later row in both forms confirms that they model the same sequence.
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