Accurate mass-interpolation and mass-asymptotic formulas are derived for one- and two-center three-body ions with unit charges. The derived formulas are applied to predict accurate numerical values of the total energies of the ground (bound) 1(1)S(L = 0)-states in one-center atomic ions X(+)e(-)e(-) and analogous ground (bound) 1s sigma-states in the two-center, quasi-adiabatic (or quasi-molecular) X(+)X(+)e(-) ions. We also discuss a few problems which currently remain unsolved for the Q(-1) expansions constructed for the ground (bound) states in few-electron atoms and ions.