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:

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

26

step-by-step explanation: