Answer
$5,-6,7,-8$
Work Step by Step
Need to find the first four terms of $a_n={(-1)^{n+1}}{(n+4)}$ when $n=1,2,3,4$
Thus, $a_1={(-1)^{1+1}}{(1+4)}=5$
$a_2={(-1)^{2+1}}{(2+4)}=-6$
$a_3={(-1)^{3+1}}{(3+4)}=7$
$a_4={(-1)^{4+1}}{(4+4)}=-8$
Hence, the first four terms are: $5,-6,7,-8$