Answer:
The sum of the series is: -66
Step-by-step explanation:
We can use the formula for a partial sum [tex]S_n[/tex] of a geometric series of n terms, with first term [tex]a_1[/tex] and ratio r:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
which in our case translates into:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}\\S_5=\frac{-96(1-(-\frac{1}{2}) ^5)}{1-(-\frac{1}{2}) }\\S_5=\frac{-96(1+\frac{1}{32} )}{1+\frac{1}{2} }\\S_5=\frac{-96(\frac{33}{32} )}{\frac{3}{2} }\\S_5=-\frac{96*11}{16} \\S_5=-66[/tex]
