Answer:
- 1364
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
4[tex](-2)^{n-1}[/tex] ← is an n th term
with a = 4 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], thus
[tex]S_{10}[/tex] = [tex]\frac{4((-2)^{10}-1) }{-2-1}[/tex]
= [tex]\frac{4(1024-1)}{-2-1}[/tex]
= [tex]\frac{4(1023)}{-3}[/tex]
= [tex]\frac{4092}{-3}[/tex]
= - 1364
