# How to Graph a Geometric Series

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Graphing a geometric series is something that you do with the sum of all numbers up to the nth term in the sequence. Graph a geometric series with help from an experienced math professional in this free video clip.

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## Video Transcript

Hi, I'm Drew Moyer and this is how to graph a geometric series. A geometric series is the sum of all numbers up to the nth term of a geometric sequence which is a group of numbers that follow a specific rule. Let's look at the following geometry sequence. We have 5, 10, 20, 40, 80 and it's very easy to see the rule. Everything is doubling from the number before it. So to find the geometric series, I can use the formula S base N is equal to A times the quantity 1 minus R to the nth power over 1 minus R. A stands for the first number in your sequence, in this case 5. R stands for the rule that it's following, in this case 2 because everything is doubling and N stands for the term up to which you want to find the sum of. Let's say I want to find the sum of all the numbers up to the 5th term. So I would say S of 5 equals A which is 5 times the quantity 1 minus R which is 2 to the nth power which again is 5 over 1 minus R which again is 2 and then from there I'm just going to simplify. S of 5 is equal to 5 times the quantity 1 minus 32 over negative 1. So of 5 is equal to 5 times negative 31 over negative 1 which equals 155. So, the sum of this sequence up to the 5th term is equal to 155. To graph it, I would simply use the 155 as the Y coordinate and 5 as the X coordinate since the sum up to the 5th term is 155. So the point on this graph would be 5, 155 and then we would just repeat as necessary until we had the number of points we needed to make a graph. I'm Drew Moyer and that is how to graph a geometric series.

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