#### Answer

$d=6$
$a_5=28$
The $n^{th}$ term is given by: $a_n = 4+6(n-1)$
$a_{100} = 598$

#### 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,
$d=10-4
\\d=6$
The fifth term $a_5$ can be found by adding the common difference $6$ to the fourth term.
The fourth term of the sequence is $22$.
Thus,
$a_5 = 22+6
\\a_5=28$
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 $a=4$ and $d=6$.
Thus, the $n^{th}$ term is given by:
$a_n = 4+6(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 4+6(100-1)
\\a_{100} = 4+ 6(99)
\\a_{100} = 4+ 594
\\a_{100} = 598$