A three-level atom in $\Lambda$ configuration with multiphoton transition is confined in a single-mode optical cavity. For any transition, the time dependence of the atom-cavity system is described by a closed set of equations. The numerical solution of these equations is calculated by using a classical fourth-order Runge-Kutta method. By applying several specific conditions it has been shown that for each distinct transition, the three-level atom reveals the behavior of an effective two-level atom. The results of the three-level atomic simulations appropriately confirm the utilized approximations in the two-level atomic pattern.
