Answer
304 feet fall in tenth second
1600 feet fall in first 10 seconds
Work Step by Step
Falls 16 ft in first second
Falls 48 ft in second second
Falls 80 ft in third second
$48-16= 32$
$80-48 = 32$
This is an arithmetic sequence with $a_1 = 16$, $n=10$ and $d= 32$
We can use the $S_n$ formula to find the sum of the finite sequence.
$S_n = (n/2) * (2a+(n-1)*d)$
$S_{10} =(10/2)*(2*16+(10-1)*32)$
$S_{10} = 5*(32 + 9*32)$
$S_{10} = 5*(1*32 + 9*32)$
$S_{10} = 5*(10*32)$
$S_{10} = 1600$
$a_{10} = a_1 + (n-1)*d$
$a_{10} = 16 + (10-1)*32$
$a_{10} = 16 + 9*32$
$a_{10} = 16 + 288$
$a_{10} = 304$
