You can find the sum of the first n terms of a geometric sequence using the formula:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]1. First, let's calculate r:
[tex]\begin{gathered} r_1=18-(-6)=24 \\ r_2=-6-2=-8 \\ r=-\frac{8}{24}=-\frac{1}{3} \end{gathered}[/tex]Replacing the values in the formula, (n=7 , r=-1/3) we get that:
[tex]S_n=13.51[/tex]2. Let's calculate r:
[tex]\begin{gathered} r_1=324-54=270 \\ r_2=54-9=45 \\ r=\frac{r_2}{r_1}=\frac{45}{270}=\frac{1}{6} \end{gathered}[/tex]Using the formula with the data we have, (n=6 , r=1/6) we get that
[tex]S_n=388.79[/tex]