Abstract
Systems of linear equations that are written in a standard form with coefficients occurring as consecutive terms of arithmetic or geometric sequences are algebraically and geometrically‐graphically explored. The solution of such systems, in particular, the arithmetic sequence‐coefficient type reveals interesting patterns. The existence of a special point in the plane, and a special line in space is found and their mathematical properties are investigated and proved. The pedagogical‐educational features of the overall activity are discussed and recommended as a worthwhile mathematical task for high school students and for both preservice and inservice mathematics teachers.
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