Time Complexity: Big-O
Here are the values of $j$ at the end of each iteration:
$$
1,3,6,10,15,21,28,36,45,55,\ldots
$$
More generally, after $t$ iterations, $j = 1 + \cdots + t = \binom{t+1}{2} = \Theta(t^2)$. Therefore the loop halts after $\Theta(\sqrt{n})$ iterations.