This article presents a finite-time heterogeneous cyclic pursuit scheme that ensures consensus among agents modeled as integrators. It is shown that for the proposed consensus scheme, even when the gains are nonidentical, consensus results within a finite time, provided all the gains are positive or even if one gain is negative, subject to a lower bound. An algorithm is presented to compute the consensus value and consensus time for a given set of positive gains and initial states of the agents. The set of values, where consensus can occur, by varying the gains, has been derived and a second algorithm aids in determining the positive gains that enable consensus at any point in the aforementioned set, at a given finite time. As an application, the finite-time consensus in line-of-sight rates, over a cycle digraph, for a group of interceptors is shown to be effective in ensuring co-operative collision-free interception of a target, for both constant speed as well as realistic time-varying-speed models of the interceptors. Simulations the theoretical results.