Spin state energies were calculated for a linear chain composed of a doublet radical and a biradical with a triplet ground state by numerical diagonalization of finite-size Heisenberg spin Hamiltonian. When all the intermolecular antiferromagnetic interactions couple the S=1/2 sites uniformly, a ferrimagnetic-like ground state appears. This finding is consistent with the simple picture of antiparallel alignment of different S’s. On the other hand, quasi-degenerate low-lying excited states appear as the spatial symmetry of intermolecular antiferromagnetic interactions is lowered. The quasi-degeneracy breaks the stability of the ferrimagnetic-like ground state. This result gives a qualitative explanation of the susceptibility and the spin-spin relaxation time measured for a nitronylnitroxide-based molecular crystal composed of an S=1/2 and S=1 molecules. The instability of the ferrimagnetic-like ground state is inherent in multi-centered antiferromagnetic interactions between the open-shell organic molecular systems, suggesting a prerequisite for purely organic ferrimagnetic ordering.