# A series of points

Geometry Level pending

The abscissa and ordinates of $$n$$ points in an arithmetic progression have their first term as $$a$$ and have common differences of 1 and 2, respectively.

If the algebraic sum of perpendiculars from these points on a variable line which always passes through the point $$\left(\dfrac{13}{2}, 11 \right)$$ is zero, then evaluate $$\left|a-n\right|$$.

×