Complex conductivity of the topological insulator (TI) Bi_{2  −  x}Sb_xTe_{3  −  y}Se_y samples of various thicknesses and chemical compositions is studied by terahertz time-domain spectroscopy method in the range 0.5 to 2.5 THz. For the first time, a decrease in conductivity in the terahertz range has been observed as the chemical composition approaches the Ren’s curve. The generalized approximate expressions are obtained for complex conductivity with account of the lowest Eu1-phonon mode. Calculations of the Fermi energy and concentration of bulk carriers are performed. Based on the experimental data, an estimate of conductance of the topological states is obtained. The results can be useful in developing terahertz devices based on the specific surface transport in TIs.