We use the density matrix renormalization group (DMRG) method to study the ground and low-lying excited states of three kinds of uniform and dimerized alternating spin chain. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of these systems. We consider a 2N-site system with spins and alternating from site to site and interacting via a Heisenberg antiferromagnetic exchange. The three systems studied correspond to being equal to and ; all of them have very similar properties. The ground state is found to be ferrimagnetic with total spin . We find that there is a gapless excitation to a state with spin , and a gapped excitation to a state with spin . The DMRG analysis shows that the chain is susceptible to a conditional spin - Peierls instability. Furthermore, our studies of the magnetization, magnetic susceptibility and specific heat show strong magnetic field dependences. The product shows a minimum as a function of temperature T at low magnetic fields; the minimum vanishes at high magnetic fields. This low-field behaviour is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature, and the height of the maximum increases sharply at high magnetic fields. Although all three systems show qualitatively similar behaviour, there are some notable quantitative differences between the systems in which the site spin difference, , is large and small respectively.