Answer:
[tex]S_{7}[/tex] = - 129
Step-by-step explanation:
The terms in the series are the terms of a geometric progression with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^n)}{1-r}[/tex] : r ≠ 1
where r is the common ratio and a the first term
here r = [tex]\frac{24}{-12}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2 and a = - 3
[tex]S_{7}[/tex] = [tex]\frac{-3(1-(-2)^7}{1-(-2)}[/tex]
= [tex]\frac{-3(1-(-2)^7}{1-(-2)}[/tex]
= [tex]\frac{-3(1-(-128))}{3}[/tex] = - 129
