Response theory calculations in the random phase approximation are applied to linear polarizabilities and second hyperpolarizabilities of 1-, 2-, and 3-dimensional hydrogen-terminated silicon clusters. Successive enlargement of the clusters to embody on the order of 50 silicon atoms plus bond-saturating hydrogen atoms allows for extrapolation to bulk values of individual silicon atom contributions in the 1D and 3D cases. Modern effective core potentials are shown to provide excellent approximations to the all-electron values in all cases; errors for both polarizabilities and hyperpolarizabilities are on the order of 1%. The findings indicate considerable time savings in predictions of the electric polarizability properties of elements beyond the first row atoms.