AP and Geometry, seems nice

Abcissae and ordinates of $n$ given points are in $AP$ with first term $a$ and common difference $1$ and $2$ . If algebraic sum of perpendiculars from these given points on a variable line which passes through the point $\large ( \dfrac{13}{2} ,11)$ is $0$ then the values of $a$ and $n$ are?

NOTE -Input your answer as the sum of the values of $a$ and $n$ .