1. The problem states the sequence $x_n = cn + d$, where $c$ and $d$ are constants. 2. This is an arithmetic sequence, where each term increases by a constant difference $c$. 3. The general formula for the $n$-th term of an arithmetic sequence is: $$x_n = a + (n-1)d$$ where $a$ is the first term and $d$ is the common difference. 4. In this problem, the formula is given as $x_n = cn + d$, which can be rewritten as: $$x_n = c n + d$$ 5. Here, $c$ represents the common difference between terms, and $d$ is a constant offset. 6. To understand the behavior of the sequence, note that as $n$ increases, $x_n$ changes linearly with slope $c$. 7. If $c > 0$, the sequence increases; if $c < 0$, it decreases; if $c = 0$, the sequence is constant. 8. The sequence is linear in $n$, so its graph is a straight line with slope $c$ and intercept $d$. Final answer: The sequence $x_n = cn + d$ is an arithmetic sequence with common difference $c$ and initial offset $d$, representing a linear function of $n$.