Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 264 feet long, and the supports increase in length by 2 feet with each support
(from 8 feet to 264 feet), what is the total length of all the supports?
A) 34,816 ft
B) 34,824 ft
C) 34,822 ft
D) 34,826 ft

Question

Quizplus · Accepted Answer

The total length of all the supports can be found using the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $a_1 = 8$ feet, $a_n = 264$ feet, and the common difference $d = 2$ feet. To find $n$, we use the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n - 1)d$. Substituting $264 = 8 + (n - 1)2$, we solve for $n$ to find the number of supports. Solving, $n = 129$. Substituting back into the sum formula, $S_n = \frac{129}{2}(8 + 264)$, we get the total length as 34,824 feet.

Use the Sequence Feature of a Graphing Calculator to Evaluate