Find the term number that equals -3x in the arithmetic sequence x, x/2, 0, -x/2, ...

The given sequence is $x, \frac{x}{2}, 0, -\frac{x}{2}, \dots$
Let's find the difference between consecutive terms:
$a_2 - a_1 = \frac{x}{2} - x = -\frac{x}{2}$
$a_3 - a_2 = 0 - \frac{x}{2} = -\frac{x}{2}$
$a_4 - a_3 = -\frac{x}{2} - 0 = -\frac{x}{2}$
Since the difference is constant, this is an arithmetic sequence with the first term $a_1 = x$ and common difference $d = -\frac{x}{2}$.

The formula for the $n$-th term of an arithmetic sequence is $a_n = a_1 + (n-1)d$.
We want to find which term $a_n$ is equal to $-3x$.
Substitute $a_n = -3x$, $a_1 = x$, and $d = -\frac{x}{2}$ into the formula:

First, subtract $x$ from both sides:

Assuming $x \neq 0$, we can divide both sides by $-x$:

Multiply both sides by 2:

Add 1 to both sides:

So, the 9th term in the sequence is equal to $-3x$.

The term is the 9th term.