Question

A stone nudged off the Royal Gorge Bridge near Cajón 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, ... 4.

Answer 1

we have the sequence

16, 48, 80, ..

so

a1=16 ------> first term

a2=48 -----> second term

a3=80 ----> third term

step 1

Find the common difference d

a2-a1=48-16=32

a3-a2=80-48=32

so

the value of d=32

step 2

Find the explicit formula

f(n)=f(1)+(n-1)d

we have

f(1)=16

d=32

substitute

f(n)=16+(n-1)*32

Simplify

f(n)=16+32n-32

f(n)=32n-16

step 3

Find the distance traveled in the 5th second

so For n=5

substitute in the formula

f(5)=32*5-16

f(5)=144 feet