  Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground
state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and
$s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the
thermodynamics of the delta-chain with competing ferro- and antiferromagnetic
interactions. We study both classical and quantum versions of the model. The
classical model is exactly solved and quantum effects are studied using full
diagonalization and a finite temperature Lanczos technique for finite
delta-chains as well as modified spin wave theory. It is shown that the main
features of the magnetic susceptibility of the quantum spin delta chain are
correctly described by the classical spin model, while quantum effects
significantly change the low-temperature behavior of the specific heat. The
relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.
