Solve the problem.
-A new exhibit is scheduled to open at the local museum. Museum officials expect that 7000 people will visit the exhibit in its first week, and that the number of visitors will drop by 10 people per week after the first week during the first 6 months. Find the total number of visitors expected in the exhibit's first 7 weeks.
A) 48,790 visitors
B) 41,850 visitors
C) 48,730 visitors
D) 34,850 visitors

Question

Quizplus · Accepted Answer

The total number of visitors expected in the exhibit's first 7 weeks can be calculated using the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}[2a + (n-1)d]$, where $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. Here, $n = 7$, $a = 7000$, and $d = -10$. Thus, $S_7 = \frac{7}{2}[2(7000) + (7-1)(-10)] = \frac{7}{2}[14000 - 60] = \frac{7}{2}[13940] = 48790$.

Solve the Problem. -A New Exhibit Is Scheduled to Open at the Local