Mathematics - PearsonAccess.com

Objective 2Students in a math class used a pattern to construct a series ofincreasingly larger quadrilaterals, and then they measured theperimeters of the quadrilaterals. The perimeters are given in thetable below.QuadrilateralPosition 1 2 3 4Perimeter (cm) 5 8 13 20If the pattern continues, what expression can be used to representthe perimeter of the nth quadrilateral in this series?The perimeters do not increase by a constant amount, so this is nota linear relationship.Look for a quadratic pattern.Position(n)Square ofposition(n 2 )Perimeter(cm)1 1 52 4 83 9 134 16 20The perimeter of each quadrilateral is 4 more than the square of itsposition number in the series. The perimeter of the nthquadrilateral should be n 2 4.See whether this expression works for the known values.Position n 2 4Perimeter(cm)Yes/No1 1 2 4 1 4 5 5 Yes2 2 2 4 4 4 8 8 Yes3 3 2 4 9 4 13 13 Yes4 4 2 4 16 4 20 20 YesIf the pattern continues, the perimeter of the nth quadrilateralcould be represented by the expression n 2 4.55