A semiempirical model has been used to predict the electronic photoabsorption spectra of five icosahedral fullerenes in the range C-60-C-720. The model parameters are first fixed in C-60 by fitting its calculated spectrum to the available experimental data, and then conveniently adjusted to describe the larger fullerenes. The structures observed in the calculated spectra show a tendency to smooth pi and sigma plasmons as the fullerene size increases; however other finite-size features related to the particular geometry of these molecules are still visible at higher resolution. Some consequences of the strong electron screening effects on these spectra are discussed.