Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.
Identify the domain of a sequence
Problem
In this sequence, \(a_{1}\) is the first term, \(a_{2}\) is the second term, and so on. State the domain implied by this indexing.
Big Picture
What this problem is really about
A sequence is a function whose inputs are term numbers, so its domain comes from the indexing rather than from an interval on the real line. We’ll identify the first subscript shown, follow the stated continuation of consecutive indices, and decide whether zero, negative integers, or values between integers belong. The ellipsis also tells us whether the domain ends.
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