The domain for n in the arithmetic sequence an = 4n + 1 is all real numbers. This means that you can choose any real number for n, and the sequence will still produce a valid output.
In an arithmetic sequence, n typically represents the term number, which can take on integer values starting from 1 (or 0, depending on the specific definition of the sequence). However, since the expression 4n + 1 itself does not impose any restrictions on n, we can say that the sequence can actually be defined for any real number.
To summarize, while the most common interpretation allows for n to be any integer (like 1, 2, 3, etc.), in mathematical terms, the domain is more broadly considered to be all real numbers, ℝ.