This article studies how preservice teachers consider the concept of the infinite limit of a sequence in relation to their future teaching practice through the numeric-vectorial component. During the research, 27 prospective secondary education and Baccalaureate (secondary school)-level teachers were organised into groups and were asked to debate different fragments setting out the above-mentioned limit that had been extracted from textbooks from different publishers. In the analysis, phenomenology was considered in the sense defined by Freudenthal, from two possible approaches —intuitive and formal, and by applying four systems of representation: verbal, tabular, graphic, and symbolic; in addition, Elementary and Advanced Mathematical Thinking levels were considered in order to classify the phenomena chosen. Based on this analysis, we were able to determine five individual and three group level phenomenological profiles. We have used these data to offer some insights into teaching and learning of the infinite limit of a sequence from the perspective of prospective teachers.