Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.
Interpret a sequence rule in context
Problem
In a theater, \(a_{n}~=~12~+~4(n~-~1)\) is the number of seats in row \(n\) for \(n~=~1,~2,~3,~\ldots~\). Identify the index and domain, initial value, and change, then verify a contextual term.
Big Picture
What this problem is really about
Interpret the sequence index as the discrete contextual input before reading the formula’s parameters. Evaluating at the first allowed index reveals the initial amount, while increasing the index by one reveals the per-step change. We’ll attach units to both ideas and test a later term to verify the interpretation.
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