Answer
$3, 8, 15, 24, 35$
Work Step by Step
We find the first $5$ terms by plugging in $1, 2, 3, 4$, and $5$ in for $n$
$a_1 = (1)^2 + 2(1)= 3$
$a_2 = (2)^2 + 2(2)= 8$
$a_3 = (3)^2 + 2(3)= 15$
$a_4 = (4)^2 + 2(4)= 24$
$a_5 = (5)^2 + 2(5)= 35$