[tex]S_{5}[/tex] = [tex]\frac{242}{27}[/tex] = 8 [tex]\frac{26}{27}[/tex]
The sum of n terms in a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^n)}{1-r}[/tex], hence
[tex]S_{5}[/tex] = [tex]\frac{6(1-(1/3)^5)}{1-1/3}[/tex]
= [tex]\frac{6(1-1/243)}{2/3}[/tex]
= 9 ( [tex]\frac{242}{243}[/tex]) = [tex]\frac{242}{27}[/tex]
