Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.
Interpret a recursive sequence definition as a function
Problem
For \(a_{1}=10\) and \(a_{n}=a_{n-1}+3\), identify integer domain, initial input/output, recurrence operation, and first four terms.
Big Picture
What this problem is really about
A recursive sequence needs both a starting input-output pair and a rule that advances from one integer input to the next. We’ll use the initial subscript to establish the domain’s starting point, interpret the recurrence as an operation on the previous output, and apply that operation repeatedly. The generated terms will check that every part of the definition agrees.
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