Question

question
a fabric company can produce 6,100 yards of fabric per year currently. the company’s goal is to increase the amount of fabric it can produce by 400 yards each year. if the company meets its goal, how many total yards of fabric will it have produced after 7 years?
select the correct answer below:
42,600
45,500
51,100
53,900

Explanation:

Step1: Identify the arithmetic - sequence formula

The sum of an arithmetic - sequence $S_n=\frac{n}{2}(2a+(n - 1)d)$, where $n$ is the number of terms, $a$ is the first - term, and $d$ is the common difference. Here, $n = 7$, $a=6100$, and $d = 400$.

Step2: Substitute the values into the formula

$S_7=\frac{7}{2}(2\times6100+(7 - 1)\times400)$.
First, calculate the value inside the parentheses: $2\times6100+(7 - 1)\times400=12200+6\times400=12200 + 2400=14600$.
Then, calculate $S_7$: $S_7=\frac{7}{2}\times14600=7\times7300 = 51100$.

Answer:

51,100