Question

question
a fabric company can produce 10,200 yards of fabric per year currently. the companys goal is to increase the amount of fabric it can produce by 500 yards each year. if the company meets its goal, how many total yards of fabric will it have produced after 8 years?
provide your answer below:

Explanation:

Step1: Identify the arithmetic - sequence elements

The first - term $a_1 = 10200$, the common difference $d = 500$, and the number of terms $n = 8$.

Step2: Use the sum formula for an arithmetic sequence

The sum formula of an arithmetic sequence is $S_n=\frac{n}{2}[2a_1+(n - 1)d]$.
Substitute $a_1 = 10200$, $d = 500$, and $n = 8$ into the formula:
\[

$$\begin{align*} S_8&=\frac{8}{2}[2\times10200+(8 - 1)\times500]\\ &=4[20400+7\times500]\\ &=4[20400 + 3500]\\ &=4\times23900\\ &=95600 \end{align*}$$

\]

Answer:

95600