[tex]p_n=\dfrac13p_{n-1}[/tex]
[tex]\implies p_n=\dfrac13\left(\dfrac13p_{n-2}\right)=\dfrac1{3^2}p_{n-2}[/tex]
[tex]\implies p_n=\dfrac13\left(\dfrac13p_{n-3}\right)=\dfrac1{3^3}p_{n-3}[/tex]
and so on, up to
[tex]p_n=\dfrac1{3^{n-4}}p_4=\dfrac{108}{3^{n-4}}[/tex]
which means
[tex]p_6=\dfrac{108}{3^{6-4}}=\dfrac{108}9=12[/tex]
