We investigate the radial dependence of the spectroscopic properties, in particular the Mg2, <Fe> and H beta spectroscopic indices, in a sample of galaxies spanning a wide range of absolute luminosity in the Coma cluster. After allowing for the magnitude dependence of these indices, we find a significant gradient in Mg2, in the sense that galaxies in the core of the cluster have stronger Mg2. We find only weak gradients in <Fe> and H beta. Using the model grids presented in an earlier paper in this series, we attribute the Mg2 gradient to changes in metal abundance. One possible mechanism to create this abundance gradient is pressure confinement by the intracluster medium of material from Supernova driven winds early in the history of the galaxies.