Answer: The sum is 195,312
Step-by-step explanaton:
The n-th term in a geometric sequence can be written as:
An = A1*r^(n-1)
Here we have:
A1 = A1*r^(1-1) = A1 = -3
A2 = A1*r^(2-1) = -3*r = 15
r = 15/-3 = -5
A3 = A1*r^(3-1) = -3*-5^2 = -3*25 = -75
So we can conclude that the sequence is:
An = -3*(-5)^(n-1)
We want to obtain the sum of the first 8 terms.
The sum of N terms in a geometric series is:
S = A1*(r^N - 1)/(r - 1)
So we have:
S = -3*(-5^8 - 1)/(-5 - 1) = (-3/-6)*(-5^8 - 1) = 195,312