Question

Construct an explicit rule in function notation for the arithmetic sequence. Then determine the value of the given term, and explain what it means.

To package and ship an item, it costs $6.25 for the first pound and $1.25 for each additional pound. Find the 9th term, and explain what it represents.
a. Function Rule: T(n) = 6.25 + 1.25(n - 1); 9th term represents the cost to ship a 9-pound item.
b. Function Rule: T(n) = 6.25n + 1.25; 9th term represents the total cost of shipping 9 items.
c. Function Rule: T(n) = 6.25n + 1.25; 9th term represents the cost to ship a 9-pound item.
d. Function Rule: T(n) = 6.25 + 1.25n; 9th term represents the total cost of shipping 9 items.

Answer 1

The correct function rule for the cost to ship an item based on weight is T(n) = 6.25 + 1.25(n - 1). To determine the 9th term, we calculate T(9) = $16.25, which represents the cost to ship a 9-pound item.

Step-by-step explanation:

To find an explicit rule for the arithmetic sequence that represents the cost to package and ship an item, we start with the initial cost for the first pound and then add the cost for each additional pound. The formula to calculate the total cost T(n) for shipping n pounds is:

T(n) = 6.25 + 1.25(n - 1)

This formula indicates that the cost begins at $6.25 (for the first pound) and increases by $1.25 for each subsequent pound. To find the cost to ship a 9-pound item, we substitute n with 9:

T(9) = 6.25 + 1.25(9 - 1) = 6.25 + 1.25(8) = 6.25 + 10 = $16.25

The 9th term in this sequence represents the total cost of shipping an item that weighs 9 pounds.