The relationship between women's whole-number shoe sizes and foot lengths is an arithmetic sequence, where an is the foot length

Question

3 years ago

11

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)

Mathematics

2 answers:

Oksana_A [137] · Answer 1 · 2022-06-11T12:37:15+03:00

Answer:

an=7.35+ 0.33(n-1)

Step-by-step explanation:

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 n.

We are given values for n=7 and n=12 as a7=9.33 and a12=11

So, we proceed from the options and check which an satisfies these values:

an = 7.35 + 0.33(n-1)

when n = 7:

an = 7.35 + 0.33 (7-1)

an = 9.33

when n = 12:

an = 7.35 + 0.33 (12-1)

an = 10.98≈11

Hence, correct option is:

an=7.35+ 0.33(n-1)