Chapter 4.6, Problem 49E

To determine

To find: is the domain of an arithmetic sequence discrete or continuous and is the range of an arithmetic sequence discrete or continuous.

Answer to Problem 49E

Domain: Discrete.

Range: Discrete.

Explanation of Solution

Given information: Domain and range of an arithmetic sequence.

Calculation:

An arithmetic sequence is a function having domain D:

D= {1, 2, 3, 4.......} that is the whole number set and the range R:

R = $\{a_1,a_2,a_3,\mathrm{.......}\}$

Thus the domain of an arithmetic sequence is discrete as it does not involve intervals, but only positive integer numbers.

The range of an arithmetic sequence is also discrete as the any consecutive values of terms “jump” with the common difference one from another.