Even numbers from 1 to 100 are as follows
2, 4, 6, 8, 10....................., 98, 100
The sum can be calculated below
[tex]\begin{gathered} a=2 \\ S_{100}=\frac{n}{2}(a+l) \\ \end{gathered}[/tex]let find n first
[tex]\begin{gathered} 100=a+(n-1)d \\ 100=2+(n-1)2 \\ 100=2+2n-2 \\ n=\frac{100}{2} \\ n=50 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} S_{100}=\frac{50}{2}(2+100) \\ S_{100}=\frac{50}{2}(102) \\ S_{100}=2550 \end{gathered}[/tex]