Hello,
A sequence $\displaystyle (x_n)$ is a Cauchy sequence if :
$\displaystyle \forall ~ \varepsilon > 0, ~ \exists N \in \mathbb{N}, ~ \text{such that } \forall ~ p,q > N, ~ |x_p-x_q|< \varepsilon$
Note that since $\displaystyle 0<r<1$, $\displaystyle \forall ~ \delta > 0, ~ \exists ~ N \in \mathbb{N}, ~ \text{such that } \forall ~ n > N, ~ r^n < \delta$
because the limit of r^n is 0.
Now, write, assuming p>q, $\displaystyle |x_p-x_q|=|(x_p-x_{p-1})+(x_{p-1}-\dots-x_{q+1})+(x_{q+1}-x_q)|$.
Use the triangle inequality : $\displaystyle |x+y| \le |x|+|y|$
Try to rearrange all this information to answer the question