#### Answer

$d=4$
$a_5=4$
The $n^{th}$ term is given by: $a_n = -12+4(n-1)$
$a_{100} = 384$

#### Work Step by Step

The sequence is arithmetic so the terms have a common difference.
The common difference $d$ can be found by subtracting any term to the next term in the sequence.
Thus,
$d=-8-(-12)
\\d=-8+12
\\d=4$
The fifth term $a_5$ can be found by adding the common difference $4$ to the fourth term.
The fourth term of the sequence is $0$.
Thus,
$a_5 = 0+4
\\a_5=4$
The $n^{th}$ term $a_n$ of an arithmetic sequence is given by the formula $a_n = a+d(n-1)$ where $a$ = first term and $d$ = common difference.
The sequence has $a=-12$ and $d=4$.
Thus, the $n^{th}$ term is given by:
$a_n = -12+4(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = -12+4(100-1)
\\a_{100} = =12+4(99)
\\a_{100} = -12+396
\\a_{100} = 384$