Question

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

Answer 1

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