The relationship between women’s whole-number shoe sizes and foot lengths is an arithmetic sequence, where A sub n is the foot length in inches that corresponds to a shoe size of n A women’s size 7 fits a foot 9 and 1 third inches long, and a women’s size 12 fits a foot 11 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary.
Answer
A
A sub n is equal to negative 17 point 9 1 plus 2 point 9 9 times open paren n minus 1 close paren
B
A sub n is equal to 7 plus 0 point 3 3 times open paren n minus 1 close paren
C
A sub n is equal to negative 5 plus 2 point 9 9 times open paren n minus 1 close paren
D
A sub n is equal to 7 point 3 5 plus 0 point 3 3 times open paren n minus 1 close paren
Explanation
The common difference is (11 − 9⅓) ÷ (12 − 7) = ⅓ inch per shoe size, or about 0.33. Using the rounded difference, the first term is A₁ = 9.33 − 6(0.33) = 7.35. Therefore, the explicit formula is Aₙ = 7.35 + 0.33(n − 1), which is choice D.
AI-written and checked against the verified answer.