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

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An arithmetic sequence is defined by a formula that indicates how to generate its terms based on the variable n. In this case, the arithmetic sequence is given by the formula:

an = 2 + 3n + 1

First, simplify the formula:

an = 3n + 3

Now, let’s address the domain of n. The domain refers to the set of possible values that n can take. In the context of this arithmetic sequence, n typically represents the term number in the sequence, often starting from 0 or 1, depending on the context. Therefore, its values are usually non-negative integers (0, 1, 2, 3, …).

For a clearer understanding:

  • If n = 0, then a0 = 3(0) + 3 = 3.
  • If n = 1, then a1 = 3(1) + 3 = 6.
  • If n = 2, then a2 = 3(2) + 3 = 9.

Since n can increase indefinitely and does not encounter any restrictions in this arithmetic sequence formula, we can conclude that:

Domain of n: n ∈ {0, 1, 2, 3, …}

In interval notation, this can be expressed as:

Domain of n: [0, ∞)

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