Your geometric series starts with 6, and then you get the next term by multiplying the previous one by 1/3. So, the first five terms are
[tex]a_1=6[/tex]
[tex]a_2=6\cdot\dfrac{1}{3}=2[/tex]
[tex]a_3=2\cdot\dfrac{1}{3}=\dfrac{2}{3}[/tex]
[tex]a_4=\dfrac{2}{3}\cdot\dfrac{1}{3}=\dfrac{2}{9}[/tex]
[tex]a_5=\dfrac{2}{9}\cdot\dfrac{1}{3}=\dfrac{2}{27}[/tex]
And if we sum them we have
[tex]8+\dfrac{2}{3}+\dfrac{2}{9}+\dfrac{2}{27}=\dfrac{242}{27}[/tex]
