  In terms of spinless fermions and spin waves, we describe magnetic properties
of a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain which
behaves as a Haldane-gap antiferromagnet. On one hand, we employ the
Jordan-Wigner transformation and treat the fermionic Hamiltonian within the
Hartree-Fock approximation. On the other hand, we employ the Holstein-Primakoff
transformation and modify the conventional spin-wave theory so as to restore
the sublattice symmetry. We calculate the excitation gap, the specific heat,
the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice
relaxation rate with varying bond alternation. These schemes are further
applied to a bond-alternating tetramerized chain which behaves as a
ferrimagnet. The fermionic language is particularly stressed as a useful tool
to investigate one-dimensional spin-gapped antiferromagnets, while the bosonic
one works better for ferrimagnets.

Statistical Mechanics;Strongly Correlated Electrons