Three numbers in geometric progression add up to 39 and their product is 729. The smallest of them is:

Write the numbers as a/$r$, a and $ar$. Their product is $a^3=729$, so $a=9$. The sum gives $9/r+9+9r=39$, i.e. $3r^2-10r+3=0$, so $r=3$ or $r=1/3$. Either way the numbers are 3, 9 and 27, and the smallest is 3. (9 is the middle term — the one a stands for — and 27 the largest.) Check: 3 + 9 + 27 = 39 and $3\times 9\times 27=729$.