Answer: −976,563
Step-by-step explanation:
Since we have a negative constant of proportionality, the 9th term must be negative. This means our answer will be −976,563, however, I will still show the steps to get there mathematically.
We will find the sum of the geometric sequence to 9 terms with the following formula. Here, a is the first term (-3), r is the constant of proportionality (15/-3=-5), and n is the number of terms (9).
[tex]\displaystyle S_n=\frac{a(r^n-1)}{r-1}[/tex]
[tex]\displaystyle S_n=\frac{-3((-5)^9-1)}{-5-1}[/tex]
[tex]\displaystyle S_n=\frac{-3(-1,953,125-1)}{-5-1}[/tex]
[tex]\displaystyle S_n=\frac{-3(-1,953,126)}{-6}[/tex]
[tex]\displaystyle S_n=\frac{5,859,378}{-6}[/tex]
[tex]\displaystyle S_n=-976,563[/tex]
