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

Asia Patel

Mathematics

25 May, 05:53

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)

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Answers (2)

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Gia Perkins · Answer 1

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

Nasir Ingram · Answer 2

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)