Let for any three distinct consecutive terms a, b, c of an A.P, the lines a x+b y+c=0 be concurrent at the point P and Q (α, β) be a point such that…

Let for any three distinct consecutive terms $\displaystyle a, b, c$ of an A.P, the lines $\displaystyle a x+b y+c=0$ be concurrent at the point P and $\displaystyle \mathrm{Q}(\alpha, \beta)$ be a point such that the system of equations $$\begin{aligned} & x+y+z=6 \\ & 2 x+5 y+\alpha z=\beta \text { and } \end{aligned} $$ $\displaystyle x+2 y+3 z=4$, has infinitely many solutions. Then $\displaystyle (P Q)^2$ is equal to $\displaystyle \_\_\_\_$.