The relationship between men’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 men’s size 9 fits a foot 10 point 3 1 inches long, and a men’s size 13 fits a foot 11 point 7 1 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 9 plus 0 point 3 5 times open paren n minus 1 close paren
B
A sub n is equal to 7 point 5 1 plus 0 point 3 5 times open paren n minus 1 close paren
C
A sub n is equal to 10 point 3 1 plus 2 point 8 6 times open paren n minus 1 close paren
D
A sub n is equal to 9 plus 2 point 8 6 times open paren n minus 1 close paren
Explanation
From size 9 to size 13, the foot length increases by 11.71 − 10.31 = 1.40 inches across 4 size steps, so the common difference is 1.40 ÷ 4 = 0.35 inch. The size 1 term is 10.31 − 8(0.35) = 7.51 inches. Thus the explicit formula is Aₙ = 7.51 + 0.35(n − 1), which is choice B.
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