Answer
(a) $576$ ft
(b) $16n^2$
Work Step by Step
We have the sequence:
$16, 48, 80$ ...
This corresponds to an arithmetic sequence with $a=16$ and $d=32$.
(a) We find the total distance after 6 seconds (n=6):
$S_n=\frac{n}{2}[2a_1+(n-1)d]$
$S_{6}= \frac{6}{2}(2*16+5*32)=3*192=576$ ft
(b) The total distance after $n$ seconds would be:
$S_{n}= \frac{n}{2} [2*16+(n-1)32]$
$S_{n}= \frac{n}{2} [32+32 (n-1)]$
$S_{n}= \frac{n}{2} [32+32n-32]$
$S_{n}= \frac{n}{2} [32n]$
$S_{n}= 16n^2$
