Question

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

Answer 1

Answer:

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

Step-by-step 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:

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