Given the arithmetic sequence an = 2 + 4(n - 1), what is the domain for n?

Solution:

An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant.

The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d.

In arithmetic sequence n represents number of terms, i.e. a₁, a₂,... a_n

n can take values of only natural numbers.

As we know that a_n = a - d(n - 1)

From the given series,

First term of the series a is 2

Common difference d is -4

⇒ a_n = 2 + 4(n - 1)

Since d = -4, i.e. d is negative, the domain of the series n is the set of natural numbers i.e n ≥ 1.

Therefore, the domain for n is all integers where n ≥ 1.

Given the arithmetic sequence an = 2 + 4(n - 1), what is the domain for n?

Summary:

If the arithmetic sequence an = 2 + 4(n - 1), then the domain of n is all integers where n ≥ 1.