College Algebra 7th Edition

(a) $576$ ft (b) $16n^2$
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: $S_{n}= \frac{n}{2} [2*16+(n-1)32]$ $S_{n}= \frac{n}{2} [32+32 (n-1)]$ $S_{n}= \frac{n}{2} [32+32n-32]$ $S_{n}= \frac{n}{2} [32n]$ $S_{n}= 16n^2$