The sum of the even numbers between 77 and 535 is:
[tex]78+80+82+\ldots+530+532+534=70074[/tex]Now, the sum of the odd numbers between 78 and 536 is:
[tex]77+79+81+\cdots+531+533+535=70380[/tex]Thus, the sum of the even numbers between 77 and 535 is 306 less than the sum of the odd numbers between 78 and 536 because
[tex]70380-70074=306[/tex]