Find the next three terms of the sequence 3, 9, 27, 81, . . .

To find the next term in the sequence, we multiply each term by 3. Thus, the next term is $81\cdot 3 = 243$. The following term is $243\cdot 3 = \boxed{729}$. The term after that is $729\cdot 3 = \boxed{2187}$.