Solve the problem.
-A railroad bridge is built over a $V$-shaped canyon. If the supports are 7 feet long at each end, the center support is 388 feet long, and the supports increase in length by 3 feet with each support (from 7 feet to 388 feet), what is the total length of all the supports?
A) $50,175 \mathrm { ft }$
B) $50,172 \mathrm { ft }$
C) $50,169 \mathrm { ft }$
D) $50,165 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The supports form an arithmetic sequence with the first term $a_1 = 7$ and the last term $a_n = 388$, with a common difference $d = 3$. The number of terms $n$ can be found using the formula $a_n = a_1 + (n-1)d$. Solving for $n$, we get $388 = 7 + (n-1) \times 3$, which gives $n = 128$. The sum of the sequence is given by $\frac{n}{2} \times (a_1 + a_n)$, which is $\frac{128}{2} \times (7 + 388) = 50,172$.

Solve the Problem VVV -Shaped Canyon 50,175ft50,175 \mathrm { ft }50,175ft B) 50,172ft50,172 \mathrm { ft }50,172ft

Solve the Problem $V$ -Shaped Canyon $50,175 \mathrm { ft }$ B) $50,172 \mathrm { ft }$