Question

Find the sum of all even numbers from $1$ to $350$ .

Answer 1

These numbers are $2,4,6,8,.....350$

$a=2$

$d=2$

$a_n=l=350$

$a_n=a+(n-1)d$

$\Rightarrow 350=2+(n-1)2$

$\Rightarrow n=175$

$S_{175}=\frac{175}{2}(2+350)=\frac{n}{2}(a+l)$

$=\frac{175}{2}\times 352$

$=30800$.