The arithmetic sequence given by an = 3 + 9n + 1 can be simplified to an = 9n + 4. In terms of the variable n, the domain relates to the values that n can take.
In an arithmetic sequence, n typically represents the position or index in the sequence. By convention, this means that n is often a non-negative integer, so:
- n can be 0, 1, 2, 3, …
Thus, in this context, the domain for n is:
- {n | n ∈ ℕ ∪ {0}}, meaning all non-negative integers.
Moreover, if the sequence is extended beyond these values, n could theoretically take any integer value (positive or negative), but typically for arithmetic sequences, we consider only non-negative integers. Therefore, the most common domain for n in this arithmetic sequence is:
n ∈ {0, 1, 2, 3, …}
In conclusion, while the arithmetic definition allows for broader possibilities, the most standard domain for n in the context of this sequence is the set of non-negative integers.