What are the likely values of $x, y$ and $z$ in the sequence

$$
\frac{1}{2}, \frac{5}{8}, \frac{3}{4}, \frac{7}{8}, x, y, z ?
$$
By equalizing the denominators, we verify that the given sequence is equal to

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

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