Question

The sequence of the other length of the rectangles is represented by the equation: an=8+(n−1)4 a) Determine two side lengths of the tenth rectangle in the sequence. b) You are given the following areas of rectangles: 392in2, 128in2, 576in2, and 968in2 Determine which of the areas is not possible in the given sequence and explain why.

Answer 1

a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.

b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.

Explanation:

The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.