Answer:
The sum is [tex]26,660[/tex]
Step-by-step explanation:
we know that
The formula of the sum in a geometric sequence is equal to
[tex]S=a1[\frac{1-r^{n}}{1-r}][/tex]
where
a1 is the first term
r is the common ratio
n is the number of terms
we have
a1=-4, a2=24, a3=-144
Find the value of r (common ratio)
r=a2/a1
r=24/(-4)=-6
so
a1=-1
r=--6
n=6
substitute in the formula
[tex]S=(-4)[\frac{1-(-6)^{6}}{1-(-6)}][/tex]
[tex]S=(-4)[\frac{1-(-6)^{6}}{7}][/tex]
[tex]S=26,660[/tex]
