Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-A new exhibit is scheduled to open at the local museum. Museum officials expect that 9000 people will visit the exhibit in its first week, and that the number of visitors will drop by 40 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) 62,160 visitors
B) 61,920 visitors
C) 53,400 visitors
D) 44,400 visitors

Question

Quizplus · Accepted Answer

The sum of the first n terms of an arithmetic sequence is given by the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first n terms, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $a_1 = 9000$, $d = -40$ (the common difference), and $n = 7$ weeks. The nth term, $a_n$, can be found using the formula $a_n = a_1 + (n-1)d$. So, $a_7 = 9000 + (7-1)(-40) = 9000 - 240 = 8760$. Using the sum formula, $S_7 = \frac{7}{2}(9000 + 8760) = \frac{7}{2} \times 17760 = 3.5 \times 17760 = 62160$.

Use the Formula for the Sum of the First N