A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 15 seconds, find the total distance traveled.

Question

Quizplus · Accepted Answer

The total distance traveled can be found 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, $n = 15$, $a = 7$ feet, and $d = 4$ feet. Plugging these values in, we get $S_{15} = \frac{15}{2}[2(7) + (15-1)4] = \frac{15}{2}[14 + 56] = \frac{15}{2} \times 70 = 525$ feet.

A Bicycle Rider Coasts Downhill, Traveling 7 Feet the First