$\begin{align}  & p=a,\text{ }{{p}^{2}}={{a}^{2}} \\ & q=a+d,\text{    }q={{(a+d)}^{2}}={{a}^{2}}+2ad+{{d}^{2}} \\ & r=a+2d,\text{  }{{r}^{2}}={{(a+2d)}^{2}}={{a}^{2}}+4ad+4{{d}^{2}} \\ & s=a+3d,\text{  }{{s}^{2}}={{(a+3d)}^{2}}={{a}^{2}}+6ad+9{{d}^{2}} \\ & {{p}^{2}}-3{{q}^{2}}+3{{r}^{2}}-{{s}^{2}}=\left[ {{a}^{2}}-3({{a}^{2}}+2ad+{{d}^{2}})+3({{a}^{2}}+4ad+4{{d}^{2}})-({{a}^{2}}+6ad+9{{d}^{2}}) \right] \\ & {{p}^{2}}-3{{q}^{2}}+3{{r}^{2}}-{{s}^{2}}=\left[ {{a}^{2}}-3{{a}^{2}}-6ad-3{{d}^{2}}+3{{a}^{2}}+12ad+12{{d}^{2}}-{{a}^{2}}-6ad-9{{d}^{2}} \right] \\ & {{p}^{2}}-3{{q}^{2}}+3{{r}^{2}}-{{s}^{2}}=0 \\\end{align}$