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The relationship between men’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. A men’s size 9 fits a foot 10.31 inches long, and a men’s size 13 fits a foot 11.71 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary.

a^n= 7.51 + 0.35(n-1)
a^n= 9+0.35(n-1)
a^n= 9+2.86(n-1)
a^n=10.31+2.86(n-1)

So the answer would be A. I had a bit of trouble figuring this out, but then I went to Order of Operations and found it out.

So you fill in n, and I just used 9 since it's in the question. So then, subtract 1 from 9, giving you 8. Then you multiply 0.35 by 8, giving you 2.8. Now lastly, add 7.51, and you get 10.31

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wifilethbridge wifilethbridge · Answer 2 · 2019-11-28T05:23:18+01:00

Answer:

[tex]a_n=7.51+0.35(n-1)[/tex]

Step-by-step explanation:

Formula of nth term = [tex]a_n=a+(n-1)d[/tex]

We are given that an is the foot length in inches that corresponds to a shoe size of n.

We are given that A men’s size 9 fits a foot 10.31 inches long

So, n = 9

[tex]a_n = 10.31[/tex]

Substitute the values in the formula :

So, [tex]10.31=a+(9-1)d[/tex]

[tex]10.31=a+8d[/tex] ---1

We are given that a men’s size 13 fits a foot 11.71 inches long.

So, n = 13

[tex]a_n = 11.71[/tex]

Substitute the values in the formula :

So, [tex]11.71=a+(13-1)d[/tex]

[tex]11.71=a+12d[/tex] ---2

Subtract 1 form 2

[tex]11.71-10.31=a+12d-a-8d[/tex]

[tex]1.4=4d[/tex]

[tex]\frac{1.4}{4}=d[/tex]

[tex]0.35=d[/tex]

Substitute the value of d in 1

[tex]10.31=a+8(0.35)[/tex]

[tex]10.31-8(0.35)=a[/tex]

[tex]7.51=a[/tex]

Substitute the value of a and d in formula given above

[tex]a_n=7.51+(n-1)0.35[/tex]

So, the explicit formula for the arithmetic sequence is [tex]a_n=7.51+0.35(n-1)[/tex]