Variational calculation of the ground state energies of a trion, X^- and an off-center negatively charged donor, D^- in In_xAl_1-xAs/AlxGa_1-xAs quantum ring is presented. The X? ground state ener-gy is calculated within framework of the adiabatic approximation which allows us to decouple the fast electrons motion around the hole from the slow hole motion in the radial direction. The wave equation for the fast two-electron motion with the frozen-out hole in this approximation coincides with one for the off-center D^- meanwhile the dependence of the D^- energy on the distance from the center of ring gives in this approximation the potential curve for the one-dimensional hole slow motion in the radial direction.