In this study, I analyzed the problem solving processes about finding the convergence and divergence conditions of the geometric sequence using analogy and discussed the results of the problem solving pedagogically. According to the results, in order to find the convergence and divergence conditions of the sequence presented in the new form, with complex numbers, it was necessary to understand the structural similarity of convergence and divergence conditions of the already known geometric sequence comprised of real numbers. The problem solving processes were refined by analogy based on its structural similarity. In addition, students were able to re-explore solutions using dynamic geometric environment and apply similar procedures related to problem solving to search newly presented conditions. These results indicate that the dynamic geometric environment can play a significant role as a student-centered inquiry instrument in the analogy processes, which are one of the non-deductive or plausible reasoning.