Answer:
- 85
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
1[tex](-2)^{n-1}[/tex] ← is the n th term of a geometric series
with a = 1 and r = - 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
= [tex]\frac{1((-2)^{8}-1 }{-2-1}[/tex]
= [tex]\frac{256-1}{-3}[/tex]
= [tex]\frac{255}{-3}[/tex]
= - 85
