Answer:
-159964
Step-by-step explanation:
Sum of a geometric sequence is given by
S(n) = [tex]\frac{a(r^{n}-1) }{(r-1)}[/tex]
where a = first term of the sequence
r = common ratio
n = number of terms
Sequence is -4, 24, - 144........... 7 terms
here a = (-4)
r = [tex]\frac{24}{(-4)}[/tex] = (-6)
and n = 7
so sum of 7 terms
s (7) = [tex]\frac{(-4)[(-6)^{7}-1] }{(-6-1)}[/tex]
= [tex]\frac{4[(-6)^{7}-1] }{7}[/tex]
= [tex]\frac{4[-279936-1]}{7}[/tex]
= -159964
