  We apply the Lanczos method to a 2-leg ladder with mixed spins of magnitudes
$(S_1,S_2)=(1,1/2)$ located at alternating positions along the ladder. The
effect of dimerization $\gamma$ is also considered according to two different
patterns. A Spin Wave Theory (SWT) is applied to this model predicting one
gapless branch with ferromagnetic properties and another gapful branch with
antiferromagnetic nature as low energy excitations of the model. We compute the
ground state energies, Ferro- and AF-excitation gaps, magnetizations and
correlation functions as a function of $J'$ and $\gamma$ which results into a
fine estimate of the phase diagram. The Lanczos results are compared with the
SWT analysis and a qualitative agreement is found but with numerical
discrepancies. We also study numerically the Spin-Peierls instability and find
that it is conditional for any value of $ J' \in (0, 2)$ and both dimerization
patterns.
