Question

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

A. All Integers where n ≥ 0
B. All Integers where n > 1
C. All Integers
D. All Integers where n ≥ 1

Answer 1

The arithmetic sequence an = -4 + 4(n - 1) can be simplified to an = 4n - 8, and since it is defined for all integer values of n without upper or lower bounds, the domain for n is all integers.

Step-by-step explanation:

The given arithmetic sequence is an = -4 + 4(n - 1). To determine the domain for n, we need to consider all possible values that n can take such that the sequence makes sense and follows the definition of an arithmetic sequence, which is a sequence of numbers such that the difference between the consecutive terms is constant.

Here, we can rearrange the arithmetic sequence formula to simplify it as follows:

an = -4 + 4n - 4

an = 4n - 8

The sequence is defined for all integer values of n, as every integer value will produce a distinct term in the sequence. The sequence can go on indefinitely in both directions (increasing or decreasing), so there is no upper or lower bound to the index n. Therefore, the domain for n is all integers, which corresponds to choice C.