Language is a quintessential and complex human skill. One reflection is the ability to produce and understand an infinite number of new sentences (i.e., novel sequences of words) that convey richly detailed messages. This ability is ascribed to a grammatical rule system that specifies how categories of words are combined into phrases and clauses. A major question in language acquisition is how children induce the grammatical rules from experience with instances of it and without explicit correction on their production of erroneous instances. The "problem of induction" is that the grammatical rules are recursive, allowing phrases and clauses to be embedded in other phrases and clauses. For example, a recursive center-embedding rule permits a sentence such as, The dog that the girls that the boy likes feed barks. Numerous studies have investigated the rule induction process using the Artificial Grammar Learning (AGL) paradigm, which involves presenting sequences of meaningless elements generated from a rule to children or adult participants and testing their learning by having them judge the grammaticality of correct and incorrect novel sequences. Although several previous AGL studies showed that adults were unable to induce a center-embedding rule, Lai and Poletiek (2011) demonstrated successful induction if the learning experience began with simple sequences with no embedding and then progressed to sequences with one- and then two embeddings. However, a flaw in Lai and Poletiek's test sequences undermined the validity of their findings. Experiment 1 corrected this flaw, and replicated Lai and Poletiek's results, thereby providing stronger evidence that progressive learning experience supports the induction of the center-embedding rule. Experiment 2 provided further evidence by replacing the grammaticality judgment test with one that required the participants to produce completions to initial portions of sequences. Finally, Experiment 3 showed no learning when feedback was eliminated from the grammaticality judgment test, but learning still occurred with the completion test. Examination of individual performance on the completion tests in Experiments 2 and 3 revealed that not all participants induced the rule, and those that did showed a consistent trajectory: They first mastered the dependencies between the different categories of elements in the simple sequences, and then hypothesized a symmetric embedding rule before inducing the correct center-embedding rule. Thus, the results provide substantive insight into the conditions that enable the induction of a recursive grammar rule and the utility of the completion test for investigating the learning process.