Question

Calculate the sum of all even numbers from 1 to 100

Answer 1

Even numbers from 1 to 100 are as follows

2, 4, 6, 8, 10....................., 98, 100

The sum can be calculated below

`\begin{gathered} a=2 \\ S_(100)=(n)/(2)(a+l) \\ \end{gathered}`

let find n first

`\begin{gathered} 100=a+(n-1)d \\ 100=2+(n-1)2 \\ 100=2+2n-2 \\ n=(100)/(2) \\ n=50 \end{gathered}`

Therefore,

`\begin{gathered} S_(100)=(50)/(2)(2+100) \\ S_(100)=(50)/(2)(102) \\ S_(100)=2550 \end{gathered}`