The formulas for the m-th iterate ${\displaystyle (m\in N)}$ of an arbitrary homographicfunction H are determined and the necessary and sufficient conditions for a solution ofthe equation ${\displaystyle y_{m+1}=H\left(y_m\right)}$, ${\displaystyle m\in N}$ to be an infinite n-periodic sequence are given. Based on the results from this paper one can easily determine some particular solutionsof the Babbage functional equation.