Abstract Finite state automata (FSA) have a very understandable mathematical model; data can be compactly displayed using a final state automaton as well as automatically compile the system components. Sequence Pattern mining is useful for data mining &is important for a wide range of applications including the buyout sequence of consumers. Sequence Mining (SM) means the sequence patterns of the broad dataset are identified. It finds common substrings from a dataset as patterns. Most industries are interested in scan sequence patterns in their databases with massive data continuously collected. Data mining (DM) is one of the methods by which hidden patterns linked to instant sequences are recovered. We extract sequence models in sequence mining that are larger or equivalent to min support threshold value of supported patterns. In this paper, we discussed various types of automata types, automata in data mining, finite state automata, sequence mining, etc.