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

Aleena Day

15 June, 17:30

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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Justine Chavez · 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

Lillianna Mercer · 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)