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 \(\left|a-n\right|\).

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