The role of a sequence of imploding spherical and cylindrical shocks is investigated in the context of laser-driven fusion in deuterium-tritium pellets. An approximate analytical treatment of a convergent sequence of shocks is presented within the framework of gas-dynamic equations for self-similar motion. These analytical solutions are compared with the exact numerical solutions. The solutions display an explicit dependence on the relative strength between the successive shocks and the ratio of the final to the initial pressure in the shocks. These solutions are employed to estimate the fusion yield for a given input shock energy.