Hi All,

I'm struggling understanding multiple points in the following question and was hoping for some help...

Q. For any positive integer n, the sum of the first n positive integers equals: $\displaystyle \frac{n(n+1)}{2}$ what is the sum of all the even integers between 99 and 301.

Ok. so the first bit is fine. 99-301 means we are looking at even integers 100-300.

q1: Looking at the formula am i right in saying that it denotes $\displaystyle \frac{integer(next integer)}{2} = SUM$ ?

q2: The next part I find uber confusing.

$\displaystyle 2(\frac{150(150+1)}{2}) - 2(\frac{49(49+1)}{2}) $

q2a. 150 is the 150th even number, why is that important?

q2b. I have no idea where the 49 came from and why it is important?

q2c: we are dividing by 2, I understand 2 is an even number but is this saying that if you divide ANY sum by 2 (or an even number) it will give you the sum of the even numbers in that sum?

q2d: why are we multiplying each result by 2?

It could just be that I'm not understanding the question, which is equally as important.

Thanks in Advance,