We demonstrate experimentally the enhanced THz extinction by periodic arrays of resonant semiconductor particles. This phenomenon is explained in terms of the radiative coupling of localized resonances with diffractive orders in the plane of the array (Rayleigh anomalies). The experimental results are described by numerical calculations using a coupled dipole model and by Finite-Difference in Time-Domain simulations. An optimum particle size for enhancing the extinction efficiency of the array is found. This optimum is determined by the frequency detuning between the localized resonances in the individual particles and the Rayleigh anomaly. The extinction calculations and measurements are also compared to near-field simulations illustrating the optimum particle size for the enhancement of the near-field.