In the sequence $\frac{1}{2}, \frac{5}{8}, \frac{3}{4}, \frac{7}{8}, x, y, z, \ldots$ the values of $x, y$ and $z$ are...
By equalizing the denominators, we verify that the given sequence is the same as the sequence

$$
\frac{4}{8}, \frac{5}{8}, \frac{6}{8}, \frac{7}{8}, x, y, z, \ldots
$$

Thus, the denominator is 8 and the numerators are consecutive numbers. Therefore, $x=\frac{8}{8}=1, y=\frac{9}{8}$ and $z=\frac{10}{8}=\frac{5}{4}$.