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We prove the existence and uniqueness of common fixed point for a sequence of mapping, considering each pair of mapping satisfies the contractive condition on fuzzy metric space. We also prove same for generalized fuzzy metric spaces. We give the lemma to prove the main result in generalized fuzzy metric space. In this paper we extend the theorem of Gajic [7] in fuzzy metric space as well as in generalized fuzzy metric space for sequence of mappings. We give example to explain our main result.