Answer:
- 288
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
- 144 [tex](\frac{1}{2}) ^{n-1}[/tex] is in this form
with a = - 144 and r = [tex]\frac{1}{2}[/tex]
[tex]S_{infinity}[/tex] = [tex]\frac{a}{1-r}[/tex] = [tex]\frac{-144}{1-\frac{1}{2} }[/tex] = [tex]\frac{-144}{\frac{1}{2} }[/tex] = - 288
