Three numbers in geometric progression have a sum of 39 and a product of 729. Find them.

A geometric progression has a fixed ratio $r = \dfrac{a_{k + 1}}{a_k}$, and its nth term is $a_n = a r^{n - 1}$. Dividing two terms cancels $a$. Three numbers in GP can be written $\dfrac{a}{r}$, $a$, $ar$, and $a, b, c$ are in GP when $b^2 = ac$. Growth by $p\%$ a year multiplies by $1 + \tfrac{p}{100}$ each year.