Answer
$a_n = n^2 + 1$
Work Step by Step
Let's look at the terms to see if we can find a pattern:
$a_1 = 2 = 1^2 + 1$
$a_2 = 2 + 3 = 5 = 2^2 + 1$
$a_3 = 5 + 5 = 10 = 3^2 + 1$
$a_4 = 10 + 7 = 17 = 4^2 + 1$
It looks like to get the next term, $1$ is added to the square of $n$:
$a_n = n^2 + 1$
