The low-lying electronic states of Ag-3(-)((1)Sigma(g)(+),B-3(2)), Ag-3(B-2(2),(2)A(1),B-2(1),B-4(2),(2)Sigma(u)(+),1 (2)Sigma(g)(+),2 (2)Sigma(g)(+),(2)Pi(u),(4)Sigma(u)(+)), and Ag-3(+)((1)A(1),(1)Sigma(g)(+),(3)Sigma(u)(+),(3)A(1)) are studied by ab initio calculations with the Stuttgart effective core potentials and corresponding (8s7p6d)/[6s5p3d] and (8s7p5d3f )/[6s5p3d3f] basis sets. The geometries, vibrational frequencies, and energetic splittings are obtained by the coupled-cluster method including singles and doubles (CCSD) and those including up to the noniterative triples [CCSD(T)] correlation methods with additional frozen core molecular orbitals corresponding to 4s and 4p orbitals. The results for well-studied states (Ag-3(-) (1)Sigma(g)(+);Ag-3 B-2(2),(2)A(1),(2)Sigma(u)(+);Ag-3(+) (1)A(1)) are in good agreement with previous experimental results, and therefore our results for other newly studied states are expected to be reliable. The vertical detachment energies of Ag-3(-) are obtained by the electron excitation equation-of-motion coupled-cluster (EE-EOM-CCSD) method and the average deviation from the experimental results is small without any scaling correction of the obtained values. The effect of the f-functions in the basis sets and the noniterative triples in the CCSD(T) method is discussed; the bond lengths are reduced significantly and the vertical detachment energies and ionization potentials are in much better agreement with experiment.