The arithmetic sequence defined by an = 2 + 4n – 1 can be analyzed to determine the domain of n. In this context, an arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. Here, the expression 4n – 1 suggests that n is a linear term influencing the value of an.
To find the domain for n in this arithmetic sequence, we need to consider what values n can take. Typically, in arithmetic sequences, n represents the position in the sequence and is usually a positive integer (1, 2, 3, …). However, it can also include zero, depending on how the sequence is defined. In general mathematical terms, the domain of n is often defined as:
- n >= 0 (if the first term is defined to be when n is 0, thus starting the sequence from 2).
- n > 0 (if the sequence begins from the first term corresponding to n being 1).
Thus, the most common domains for the arithmetic sequence would be:
- If the sequence starts from 0: n ∈ ℕ₀ (natural numbers including zero).
- If the sequence starts from 1: n ∈ ℕ (natural numbers excluding zero).
In conclusion, the specific definition of the sequence will guide you in identifying the appropriate domain, but it’s primarily limited to non-negative integers if focusing on standard arithmetic sequences.