One cautionary point about the use of this prompt relates to the lengths of the sides of the triangles. Students can unwittingly create impossible triangles by following their sequences (even when all three are ascending). For example, triangles with sides of lengths (5, 6, 9) (7, 8, 14) gives (9, 10, 19) on the third diagram. The sum of the lengths of the two shorter sides must be greater than the length of the longest side *and* the sum of the increases of the two shorter sides must be greater than the increase of the longest side.