What is the domain for n in the arithmetic sequence defined by a_n = 3 + 2n – 1?

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An arithmetic sequence is defined by a specific formula that allows us to find any term in the sequence, given a value of n, which typically represents the position of the term in the sequence. In this case, the formula given is:

a_n = 3 + 2n - 1

This can be simplified to:

a_n = 2n + 2

Here, n represents the index of the sequence, and it can take on various values depending on what we’re considering as valid positions in the sequence. In general, for arithmetic sequences, the domain of n is typically all non-negative integers (i.e., n = 0, 1, 2, 3, …), especially in contexts like this where we are looking at sequences that start from the first term.

However, it’s important to consider:

  • If you define n to include only positive integers, then the domain could be {1, 2, 3, …}.
  • If you expand to all integers, the domain would be {…, -2, -1, 0, 1, 2, …}.

In summary, the most conventional domain for n in this context is:

  • Non-negative integers: n ≥ 0
  • Or simply, all integers, if required: n ∈ Z

Choosing the right domain depends on your specific needs when using the arithmetic sequence, so it’s essential to clarify that when discussing the domain.

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