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