Question

The relationship between men's whole-number shoe sizes and foot lengths is an arithmetic sequence, where a, 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.
0 6, 7,514 0 35(n-1)
O a. - 9-0 35(n-1)
O a-9-286(n-1)
O a, - 10 31-2 86(n-1)

Answer 1

A

Explanation:

I got it right on edge

Answer 2

`a =7.51+ 0.35(n - 1)`

Explanation:

The arithmetic sequence has the form:

`a =a_1 + d(n - 1)`

When a=10.31, n=9, we substitute to get:

`a_1 + 8d = 10.31....eqn1`

Similarly, when n=13 and a=11.71, we get:

`a_1 + 12d= 11.71....eqn2`

Subtract equation 1 from equation 2 to get:

`4d = 1.4`

This implies that

`d = 0.35`

Substitute into the second equation to get:

`a_1 +12(0.35) = 11.71`

Solve to get

`a_1 = 7.51`

Hence the explicit formula is:

`a =7.51+ 0.35(n - 1)`