Answer
$a_{8}= 31$
Work Step by Step
$a_{n}$ of the arithmetic sequence is $a_{n} = a_{1} + (n-1)d$
Similarly,
$a_{4} = a_{1} + (4-1)d$
$a_{4} = a_{1} + 3d$
$ a_{1} + 3d =19$ Equation $(1)$
$a_{15} = a_{1} + (15-1)d$
$a_{15} = a_{1} +14d$
$ a_{1} +14d = 52$ Equation $(2)$
Subtracting Equation $(1)$ from Equation $(2)$
$ a_{1} +14d - a_{1} - 3d = 52 - 19$
$11d = 33$
$d = 3$
Substituting $d$ value in Equation $(1)$
$ a_{1} + 3d =19$
$ a_{1} + 3(3) =19$
$ a_{1} + 9 =19$
$ a_{1} =19 -9$
$ a_{1} =10$
Using $ a_{1} $ and $d$ values,
$a_{8}= a_{1} + (8-1) d$
$a_{8}= 10+7(3)$
$a_{8}= 21+10$
$a_{8}= 31$
