Answer
a. $576$ ft
b. $16n^{2}$ ft
Work Step by Step
The given sequence
16, 48, 80,$...$
... has a common difference, $80-40=48-16=32,$
so it is an arithmetic sequence
with $a=16$
and $d=32$.
a.
The total distance after 6 seconds is the sum of the first 6 terms:
$S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]$
$S_{6}=\displaystyle \frac{6}{2}(32+5\cdot 32)=3\cdot 192=576$ ft.
(b) The total distance after $n$ seconds is
$S_{n}=\displaystyle \frac{n}{2} [32+32 (n-1)]$
$= \displaystyle \frac{n}{2} [32+32n-32]$
$=\displaystyle \frac{32n^{2}}{2}$
$=16n^{2}$ ft
