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.
the 9th term is
the total shipping cost of a 9 - pound package is $

Explanation:

Step1: Identify the first - term and common - difference of the arithmetic sequence

The first - term $a_1$ of the arithmetic sequence is the cost for the first pound. So, $a_1 = 6.25$. The common - difference $d$ is the cost for each additional pound, so $d = 1.25$.

Step2: Write the explicit rule for the arithmetic sequence

The explicit rule for an arithmetic sequence in function notation is $a_n=a_1+(n - 1)d$. Substituting $a_1 = 6.25$ and $d = 1.25$ into the formula, we get $a_n=6.25+(n - 1)\times1.25$. Simplifying this gives $a_n=6.25 + 1.25n-1.25=1.25n + 5$.

Step3: Find the 9th term

Substitute $n = 9$ into the explicit formula $a_n=1.25n + 5$. Then $a_9=1.25\times9 + 5=11.25+5=16.25$.

Answer:

The 9th term is $16.25$. It represents the total cost to package and ship a 9 - pound item. The total shipping cost of a 9 - pound package is $\$16.25$.