Answer
$a_{1}=-2;a_{2}=4;a_{3}=-6;a_{4}=8;a_{5}=-10$
Work Step by Step
$a_{1}=\left( -1\right) ^{1}\times \left( 2\times 1\right) =-2;$
$a_{2}=\left( -1\right) ^{2}\times \left( 2\times 2\right) =4;$
$a_{3}=\left( -1\right) ^{3}\times \left( 2\times 3\right) =-6$
$a_{4}=\left( -1\right) ^{4}\times \left( 2\times 4\right) =8;$
$a_{5}=\left( -1\right) ^{5}\times \left( 2\times 5\right) =-10$