Answer
$d=3$
$a_{n}=3n-\left( t+3\right) $
$ a_{5} =-t+12 ;$
$a_{100}=-t+297$
Work Step by Step
$d=a_{n+1}-a_{n}=\left( -t+3\right) -\left( -t\right) =-t+6-\left( -t+3\right) =3$
$a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=-t$
$a_{n}=a+\left( n-1\right) d=-t+\left( n-1\right) \times 3=-t-3+3n=3n-\left( t+3\right) $
$a_{n}=3n-\left( t+3\right) \Rightarrow a_{5}=3\times 5-\left( t+3\right) =12-t;a_{100}=3\times 100-\left( t+3\right) =-t+297$
