9514 1404 393
Answer:
S9 = 52,429
Step-by-step explanation:
The sum is given by the formula ...
[tex]S_n=a_1\times\dfrac{r^n-1}{r -1}[/tex]
The first term of this series is a1 = 1. The common ratio is r = -4/1 = -4. You want the sum for n = 9 terms. Putting these values into the formula gives ...
[tex]S_{9}=1\times\dfrac{(-4)^{9}-1}{(-4) -1}=\dfrac{-262144-1}{-5}=\boxed{52429}[/tex]
