Question

Find the sum of all of the odd integers between $200$ and $400$

Answer 1

$201+203+......+399$ [It is an A.P. with $d=2$]

$a=201$; $a_n=399$

$\Rightarrow a_n=a+(n-1)d\Rightarrow (n-1)=\frac{399-201}{2}\Rightarrow n=100$

$\Rightarrow S_n=\frac{n}{2}[a+a_n]=50[201+399]=30000$.