Answer:
≈ 486.02
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
where a is the first term and r the common ratio
Here a = 324 and r = [tex]\frac{-108}{324}[/tex] = - [tex]\frac{1}{3}[/tex], thus
[tex]S_{9}[/tex] = [tex]\frac{324(1-(-1/3)^9)}{1-\frac{1}{3} }[/tex]
= [tex]\frac{324(1+\frac{1}{19683}) }{\frac{2}{3} }[/tex]
= 486([tex]\frac{19684}{19683}[/tex] ) ≈ 486.02 ( to the nearest hundredth )
