Denominators in Convergents of Continued Fraction

Question

Let $\theta, \theta'$ be the roots of the equation $x^2-ax-1=0$, where $a$ is a positive integer and $\theta >0$. Show that the denominators in the convergents to $\theta$ are given by $q_{n-1}=(\theta^n-\theta'^{n})/(\theta-\theta')$. Verify that the Fibonacci sequence 1, 1, 2, 3, 5,... is given by $q_0, q_1,...$ in a special case.