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 8 seconds, find the total distance traveled.

Question

Quizplus · Accepted Answer

This is an arithmetic sequence problem where the distance traveled each second forms an arithmetic sequence with the first term $a = 7$ feet and the common difference $d = 4$ feet. The total distance traveled in $n = 8$ seconds can be found using the formula for the sum of the first $n$ terms of an arithmetic sequence: $S_n = \frac{n}{2}[2a + (n-1)d]$. Substituting the given values, we get $S_8 = \frac{8}{2}[2(7) + (8-1)4] = 4[14 + 28] = 4[42] = 168$ feet.

A Bicycle Rider Coasts Downhill, Traveling 7 Feet the First