Given the arithmetic sequence an = 5 + 2(n − 1), what is the domain for n?
all integers
all integers where n ≥ 0
all integers where n > 1
all integers where n ≥ 1

Since this is an arithmetic sequence, the first thing to note is that n is both a variable within the definition of the sequence, and it also is the index value too. As an index value, it has to be an integer as there is no such thing as a fractional index. Next, all indexes start from the number 0, because the 0th term is the initial value of the sequence. Therefore, n must also start with 0. All subsequent terms in the sequence are then terms with higher index values, so n will always be greater than or equal to 0. A quick check on the equation will also show that there is no other limiting factor on n. Thus, the correct answer is "All integers where n≥0".

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