The relationship between women's whole-number shoe sizes and foot lengths is an arithmetic sequence, where an is the foot length in inches that corresponds to a shoe size of a n. A women's size 7 fits a foot 9 1/3 inches long, ands women's size 12 fits a foot 11 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary. an=-17.91 + 2.99 (n-1), an=-5+2.99 (n-1), an=7+0.33 (n-1), an=7.35 + 0.33 (n-1)

Question

Mathematics

Rodolfo Buchanan

12 June, 15:59

The relationship between women's whole-number shoe sizes and foot lengths is an arithmetic sequence, where an is the foot length in inches that corresponds to a shoe size of a n. A women's size 7 fits a foot 9 1/3 inches long, ands women's size 12 fits a foot 11 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary. an=-17.91 + 2.99 (n-1), an=-5+2.99 (n-1), an=7+0.33 (n-1), an=7.35 + 0.33 (n-1)

+3

Answers (2)

Know the Answer?

Jadyn · Answer 1

In an arithmetic sequence:

a12-a7 = 11-9.33=1.67

a12 = a7 + 5 d

5d = 1.67

d = 1.67: 5 = 0.33

a7 = a1 + 6 d

9.33 = a1+6 * 0.33

a1 = 9.33 - 1.98 = 7.35

The formula an = a1 + d (n-1)

Answer: D) an = 7.35 + 0.33 (n-1)

German Francis · Answer 2

Since you are already given different formulas for the foot length when given the shoe size number, one method of finding the right formula is to substitute the given values of n (shoe size number) and see if they would give out the corresponding value of an (foot length in inches). This is done below:

an = 7.35 + 0.33 (n-1)

Using n = 7:

an = 7.35 + 0.33 (7-1)

an = 9.33 / / OK

Using n = 12:

an = 7.35 + 0.33 (12-1)

an = 10.98 / / OK