Question

In a women's shoe size and foot length arithmetic sequence, a size 3 fits an 8-inch foot, and a size 7 fits a 9.3-inch foot. What is the common difference of the arithmetic sequence?

Answer 1

The common difference of the arithmetic sequence representing women's shoe size and foot length is 0.325 inches per shoe size.

Step-by-step explanation:

To determine the common difference of the arithmetic sequence that represents women's shoe sizes and their corresponding foot lengths, consider the given sizes: a size 3 for an 8-inch foot and a size 7 for a 9.3-inch foot. An arithmetic sequence has a constant difference between consecutive terms. The difference in shoe size from size 3 to size 7 is 4 sizes (7 - 3), and the corresponding difference in foot length is 1.3 inches (9.3 inches - 8 inches).

To find the common difference, divide the change in foot length by the change in size numbers:

Common difference = (9.3 inches - 8 inches) / (7 - 3) = 1.3 inches / 4 = 0.325 inches per shoe size.

Therefore, the common difference of the arithmetic sequence is 0.325 inches per shoe size.