Answer
$a_{1}=2;a_{2}=-3;a_{3}=4;a_{4}=-5;a_{5}=6$
Work Step by Step
$a_{1}=\left( -1\right) ^{1-1}\left( 1+1\right) =2;$
$a_{2}=\left( -1\right) ^{2-1}\left( 2+1\right) =-3;$
$a_{3}=\left( -1\right) ^{3-1}\left( 3+1\right) =4$
$a_{4}=\left( -1\right) ^{4-1}\left( 4+1\right) =-5;$
$a_{5}=\left( -1\right) ^{5-1}\left( 5+1\right) =6$
