Using an isobaric method,the symmetry-energy coefficient (asym) of a neutron-rich nucleus is obtained from experimental binding energies.The shell effects are shown in asym*/A ≡ 4asym/A of nuclei.A (sub)magic neutron magic number N =40 is suggested in a very neutron-rich nucleus,and asym*/A of a nucleus is found to decrease when its mass increases.The asym*/A of a very neutron-rich nucleus with large mass saturates.The volumesymmetry coefficients (bv) and surface-symmetry coefficients (bs) of a neutron-rich nucleus are extracted from asym*/A by a correlation asym*/A =bv/A - bs/A4/3.It is found that bv and bs decrease when the nucleus becomes more neutron-rich,and tend to saturate in the very neutron-rich nucleus.A linear correlation between bv and bs is obtained in nuclei with different neutron-excess I,and bv of I ＞ 7 nuclei is found to coincide with the results of infinite nuclear matter asym =32 ± 4 MeV,and bs/bv of the nucleus is found to coincide with the results of the finite-range liquid-drop model results.