A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance it travels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another 80 feet. The distances traveled each second form an arithmetic sequence: 16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
What is the first term of the sequence?
What is d, the common difference?
Write the explicit formula in function notation. Use f(n) = f(1) + (n – 1)d, where f(1) represents the first term.
Use the explicit formula to find the distance the stone travels in the 5th second.