For a geometric series explain how you can tell if the series converges or diverges as you keep adding an infinite number of terms to the series. be sure that your explanation is clear on what it means to converge or diverge. show using an example(s).

It will converge if the common factor  r  is between 0 and 1.
For example:-
 A GS with  first term a1 = 2  and d = 1/2,   the  terms are:-

2 , 1 , 1/2, 1/4, 1/8,1/16 and so on

Each term gets smaller and smaller and they will become very small - close to 0.   The sum will converge to a certain value also.
In this case it will converge to  2 /( 1 - 1/2) = 4

If d > 1  the terms will increase without bounds and the sum gets bigger and bigger . The series  diverges.

for example  2, 8, 32, 128, 512   where a1 = 2 and d = 4.

Abit confused about what you mean, but i think you might be referring to slope intercept form: y = mx + bin that case b, or the y intercept is already given.(0,-1)find the slope by using the formulay2 - y1/x2 - x1the final slope will be 4/2, equivalent to 2.now your equation should look like thisy = 4/2x -1sorry if this didn’t you out!