Find the sum of all even number between 1 to 350.

Answer

The sum of all even numbers between 1 and 350 is 30450.

Explanation

The even numbers 1 and 350 are 2, 4, 6, …., 348.
Here, `a=t_(1)=2,d=t_(2)-t_(1)=4-2=2,t_(n)=348`. First we find `n`.
`t_(n)=a+(n-1)d` ...(Formula)
`therefore348=2=(n-1)xx2` …(Substituting the l=values) ,
`therefore348-2=(n-1)xx2`
`therefore(n-1)xx2=346" "thereforen-1=(346)/(2)" "thereforen-1=173`
Now, `S_(n)=(n)/(2)(t_(1)+t_(2))`
`=(174)/(2)(2+348)`
`thereforeS_(174)=87xx350=30450`