Find the sum

the first odd integer is $13$ and the last odd integer is $781$

The series of numbers form an arithmetic progression with a common difference of $2$ . Let $a_1=13$ and $a_n=781$ .

$a_n=a_1+(n-1)d$ $\implies$ $781=13+(n-1)2$ $\implies$ $384=n-1$ $implies$ $n=385$

$s=\dfrac{n}{2}(a_1+a_n)$ $\implies$ $s=\dfrac{385}{2}(13+781)=$ $\boxed{152845}$