Find the sum of the geometric sequence - 3,15,-75,375, ... when there are 8 terms

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