Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.
Decide whether explicit and recursive rules define the same sequence
Problem
Compare explicit \(a_{n}=5+2(n-1)\), \(n\ge~1\), with recursive \(a_{1}=5\), \(a_{n}=a_{n-1}+2\).
Big Picture
What this problem is really about
Different-looking formulas define the same sequence only if they agree at every allowed index. We’ll first compare their domains and initial outputs, then identify the term-to-term change in each representation and generate several corresponding terms. Matching change alone is insufficient when starting values or indexing differ, so all three checks matter.
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