This geometric progression is given by 6 + 2 + 2/3 + 2/9 + ... + a6
We can calculate common ratio r with any two terms a_n and a_n+1 as follows:
[tex]r=\frac{a_{n+1}}{a_n}[/tex]
With the terms a1 = 6 ans a2 = 2 we have r = 2/6 = 1/3
Therefore, we have:
[tex]S_6=\frac{a_1(1-r^6)}{1-r}=\frac{6\cdot(1-(1/3)^6)}{1-1/3}=8.99[/tex]
