Question

Pn=1/3pn-1 and p4=108 , then p6= ? please show steps

Answer 1

`p_n=\frac13p_(n-1)`

`\implies p_n=\frac13\left(\frac13p_(n-2)\right)=\frac1{3^2}p_(n-2)`

`\implies p_n=\frac13\left(\frac13p_(n-3)\right)=\frac1{3^3}p_(n-3)`

and so on, up to


`p_n=\frac1{3^(n-4)}p_4=(108)/(3^(n-4))`

which means


`p_6=(108)/(3^(6-4))=\frac{108}9=12`