Given:
2+4+6+8+10+.....+50
[tex]2+4+6+10+\cdots+50=2(1+2+3+\cdots+25)[/tex]Let the sum of the first n natural numbers be
[tex]S_n=\frac{n(n+1)}{2}[/tex]Therefore the sum of first 25 positive even numbers is
[tex]2S_n=\frac{2n(n+1)}{2}[/tex][tex]2S_n=n(n+1)[/tex]Therefore,The sum is the product of the number of terms and the number of terms plus one.
Option B is the correct answer.