Question

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.

Answer 1

Answer:

Explicit formula for the sequence will be f(x) = 7.16 + 0.35n

Step-by-step explanation:

Step-by-step explanation:

As we know explicit formula of an arithmetic mean is given by

f(x) = a + (n-1)d

where a = first term of the sequence

n = number of term

d = common difference

Now it has been given that a men's size 9 fits a foot 10.31 inches long, means in an arithmetic sequence 9th term is 10.31. So by explicit formula

f(9) = a + (9-1)d = 10.31

⇒ a + 8d = 10.31-----(1)

Now from second statement

f(13) = a + (13-1)d = 11.71

⇒a + 12d = 11.71---------(2)

Now we subtract equation 1 from 2.

(a + 12d) - (a + 8d) = 11.71 - 10.31 = 0.40

4d = 1.40

d = 1.40/4 = 0.35

By putting the value of d in equation 1

a = 10.31 - 2.8 = 7.51

Finally we get the explicit formula of arithmetic formula as

f(x) = 7.51 + (n-1)(.35) = 7.51 + 0.35n - 0.35 = 7.16 + 0.35n

f(x) = 7.16 + 0.35n