How to find $10 + 15 + 20 + 25 + \dots + 1500$ During a test I was given the following question:
What is $$10+15+20+25+...+1490+1495+1500=?$$
After process of elimination and guessing, $ came up with an answer.  Can anyone tell me a simple way to calculate this problem without having to try to actually add the numbers?
 A: HINT: 
$(10 + 1500) + (15 + 1495) + (20 + 1490) +  \cdots + (750 + 760) + 755$.
A: 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.
A: This is probably the method C. F. Gauss would have used ;)

Factor out 5:
$5(2+3+4+5+...+297+298+299+300)$
Notice: $302/2 = 151$
$5((2+300)+(3+299)+(4+298)+(5+297)+...(149+153)+(150+152)+(151))$
$5(302+302+302+302+...+302+302+151)$
There are $(150-2+1)$ 302s, so:
$5((150-2+1)(302) + 151)$
$5((149)(302) + 151)$
$5(44998 + 151)$
$5(45149)$

The answer is $225745$.
A: Hint 3 (Gauss): $10 + 1500 = 15 + 1495 = 20 + 1490 = \cdots = 1500 + 10$.
