Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

(N/A) Let the first term of an $AP$ be $a$ and the common difference be $d$.
Given,$a_{5} = 19$ and $a_{13} - a_{8} = 20$.
Using the formula $a_{n} = a + (n - 1)d$:
For the fifth term: $a + 4d = 19$ ........$(i)$
For the difference between the thirteenth and eighth terms: $(a + 12d) - (a + 7d) = 20$
$5d = 20$
$d = 4$
Substituting $d = 4$ into equation $(i)$:
$a + 4(4) = 19$
$a + 16 = 19$
$a = 3$
The $AP$ is given by $a, a+d, a+2d, a+3d, \dots$
Substituting the values: $3, 3+4, 3+2(4), 3+3(4), \dots$
Thus,the $AP$ is $3, 7, 11, 15, \dots$