The sum to infinity of a geometric progression is 45 and its first term is 15. Find the common ratio.

From $S_\infty = \dfrac{a}{1 - r}$: $\dfrac{15}{1 - r} = 45$, so $1 - r = \dfrac{1}{3}$ and $r = \dfrac{2}{3}$. A ratio of 3 is impossible for a convergent series, and $\dfrac{1}{3}$ comes from stopping at $1 - r$ without solving for $r$.