Pleasee help mee ;-; i can't stand algebra, determine how many terms the geometric series has, and then find the sum of the series -12 -4 - 4/3 - . . . - 4/243

The series has 7 terms

Step-by-step explanation:

Geometric Series

In the geometric series, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the series:

-12, -4, -4/3, ..., -4/243

We can find the common ratio by dividing one term by the previous term:

Simplifying:

Sum of terms: Given a geometric series with first term a1 and common ratio r, the sum of n terms is:

We need to find how many terms the series has. Using the explicit formula of a geometric series:

The last term is an=-4/243 and the first term is a1=-12. Solving for n:

n=7

The series has 7 terms

Thus, the sum of the 7 terms of the series is: