What is the domain for n in the arithmetic sequence defined by a_n = 4n + 1?

The given arithmetic sequence is defined by the formula a_n = 4n + 1, where n represents the term number in the sequence.

In an arithmetic sequence, the variable n typically represents a positive integer, as it denotes the position of the term within the sequence. Therefore, the most common interpretation of the domain for n in this context is: n >= 1.

Let’s break it down further:

• Defined Terms: The terms of the sequence start from the first term, which is when n = 1.
• Mathematically: When n = 1, the first term a_1 can be calculated:
• a_1 = 4(1) + 1 = 5
• Subsequent Terms: You can find the second term when n = 2 and so forth:
• a_2 = 4(2) + 1 = 9
• a_3 = 4(3) + 1 = 13

This pattern continues indefinitely for any positive integer value of n.

In summary, the domain for n in this arithmetic sequence is defined as:

• n >= 1

This means that n can take on any integer value starting from 1 and going to infinity, allowing you to generate an infinite number of terms in the sequence.