2860.11 – Integer Sum of Unknown Length!

You're supposed to know that

$\frac{1 + 2 + 3 + \ldots + n}{2} = \frac{n(n+1)}{2}.$

So all we need to do is set

$\frac{n(n+1)}{6n} = 36.$

Cross-multiplying,

$n^2 + n = 216n,$

a quadratic equation with roots $0$ and $215$. The latter root is the answer.