Answer :

Given that S6 is 133 and the common ratio (r) is -2/3.

We know that the sum of n terms of a gp whose common ratio is less than 1 is

[tex]S_n=\frac{a(1-r^n)}{(1-r)}[/tex]

So,

[tex]\begin{gathered} 133=\frac{a(1-(-\frac{2}{3})^6)}{1-(-\frac{2}{3})} \\ 133=\frac{a(1-\frac{64}{729})}{1+\frac{2}{3}} \\ 133=\frac{a(\frac{665}{729})}{\frac{5}{3}} \\ 133=\frac{a(133)}{243} \\ a=243 \end{gathered}[/tex]

Now, we have known that the first term of the gp is 243.

So, the second term is:

[tex]ar=243\times(-\frac{2}{3})=-162[/tex]

The third term is:

[tex]ar^2=243\times(-\frac{2}{3})^2=108[/tex]

Thus, the first three terms are 243, -162, 108.