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In this paper, we investigate a tridiagonal three-species competition model with seasonal succession. The Floquet multipliers of all nonnegative periodic solutions of such a time-periodic system are estimated via the stability analysis of equilibria. Together with the Brouwer degree theory, sufficient conditions for existence and uniqueness of the positive periodic solution are given. We further obtain the global dynamics of coexistence and extinction for three competing species in this periodically forced environment. Finally, some numerical examples are presented to illustrate the effectiveness of our theoretical results.