For a fixed number a define $\displaystyle \Delta_{a} x_{n} = x_{n+1} - ax_n$. Find formula for $\displaystyle \Delta^{2}_{a}x_{n}$ and $\displaystyle \Delta^{3}_{a}x_{n}$. Express $\displaystyle \Delta_{a}x_{n}$ in terms of $\displaystyle \Delta x_n$ and $\displaystyle x_n$.

Am I suppose to find the derivative??? I'm confused.