Answer
$d=4$
$a_{n}=4n-16$
$ a_{5}=4\times 5-16=4$
$a_{100}=4\times 100-16=384$
Work Step by Step
$d=a_{n+1}-a_{n}=-8-\left( -12\right) =-4-\left( -8\right) =0-\left( -4\right) =4$
$a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=-12$
$\Rightarrow a_{n}=a+\left( n-1\right) d=-12+\left( n-1\right) \times 4=-12+4n-4=4n-16$
$a_{n}=4n-16\Rightarrow a_{5}=4\times 5-16=4;a_{100}=4\times 100-16=384$
