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An explicit equation defines a sequence by providing a direct formula to calculate the nth term without needing the previous terms, such as ( a_n = 2n + 3 ). In contrast, a recursive equation defines a sequence by specifying the first term and providing a rule to find subsequent terms based on previous ones, such as ( a_n = a_{n-1} + 5 ) with an initial condition. Essentially, explicit equations allow for direct access to any term, while recursive equations depend on prior terms for computation.

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