Hint 1 - Is there anything you can factor out of all the numbers?
Hint 2 - Do you know how to sum $1 + 2 + \cdots + n$ in a simple way?
EDIT - Your process in the comments is not wrong, but I don't feel like it's very intuitive.
I do think it's immediately clear that all the numbers in your sum above are divisible by 5. That is, we can rewrite
$$10 + 15 + 20 + \cdots + 1500 = 5(2 + 3 + 4 + \cdots + 300)$$
Maybe not as obvious, but incredibly useful to know, is that
$$1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}$$
Finally notice $2 + 3 + \cdots + 300$ is almost $1 + 2 + \cdots + 300$, and you can use the above formula to finish the problem.