We present Iron, Magnesium, Calcium, and Titanium abundances for 235 stars in the central region of the Sagittarius dwarf spheroidal galaxy (within 9.0'~=70pc from the center) from medium-resolution Keck/DEIMOS spectra. All the considered stars belong to the massive globular cluster M 54 or to the central nucleus of the galaxy (Sgr,N). In particular we provide abundances for 109 stars with [Fe/H]>=-1.0, more than doubling the available sample of spectroscopic metallicity and {alpha}-elements abundance estimates for Sgr dSph stars in this metallicity regime. We find for the first time a metallicity gradient in the Sgr,N population, whose peak iron abundance goes from [Fe/H]=-0.38 for R<=2.5' to [Fe/H]=-0.57 for 5.0<R<=9.0 arcmin. On the other hand the trends of [Mg/Fe], [Ca/Fe], and [Ti/Fe] with [Fe/H] are the same over the entire region explored by our study. We reproduce the observed chemical patterns of the Sagittarius dwarf spheroidal as a whole with a chemical evolution model implying a high mass progenitor (M_DM_=6x10^10^M_{sun}_) and a significant event of mass-stripping occurred a few Gyr ago, presumably starting at the first peri-Galactic passage after infall.