**Solution:**

Let *a* be the first term and *r* be the common ratio of the G.P.

According to the given condition,

*a*_{4} = *a* *r*^{3} = *x* … (1)

*a*_{10} = *a* *r*^{9} = *y* … (2)

*a*_{16} = *a r*^{15} = *z* … (3)

Dividing (2) by (1), we obtain

Dividing (3) by (2), we obtain

∴

**Thus, ***x*, *y*, *z* are in G. P.