#### Answer

Pattern: Divide the previous term by 2
Next term in the sequence: $\frac{x}{24}$

#### Work Step by Step

First, you must find the pattern. Each term is exactly 1/2 of the term before it, for example:
$\frac{2x}{3}$ $\times$ $\frac{1}{2}$ = $\frac{x}{3}$
$\frac{x}{3}$ $\times$ $\frac{1}{2}$ = $\frac{x}{6}$
$\frac{x}{6}$ $\times$ $\frac{1}{2}$ = $\frac{x}{12}$
To find the next term in the sequence, you must divide the last term by 2 (or multiply by $\frac{1}{2}$):
$\frac{x}{12}$ $\times$ $\frac{1}{2}$ = $\frac{x}{24}$