For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum x of all the even integers between 99 and 301?
Options.
A) 10,100  B) 20,200  C) 22,650  D) 40,200  E) 45,150
I would solve it in a different way.   First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2= 
<gadget id="calculator">202/2</gadget>
<output>101</output>
101   Average= (301+99)/2 = 400/2= 
<gadget id="calculator">400/2</gadget>
<output>200</output>
200   Sum x= Average*total count = 200*101 = 20,200   Answer is 20,200
<result>B</result>
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum x of all the even integers between 99 and 301?