3.21: AP terms forming a convergent GP

An AP has first term $a$ and common difference $d$. Its $2$nd, $14$th and $17$th terms form a convergent GP. Given $d\neq0$, find two expressions for $r$ and show $a=-17d$.

Find the value of $r$.

The first term of the GP is $q$ and $S_{\infty}=\dfrac{256}{3}$. Find $S_{20}$ of the AP.