Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the Plugging in 3/4 for, 3 for n, and 27/16 for the n th term we get: The common ratio could be either 3/2 or -3/2. In each term, the number of times a 1 a 1 is multiplied by r is one less than the number of the term. We can still use the n th term formula for a geometric sequence,, to help us with this problem. r or r 3 r 3) and in the fifth term, the a 1 a 1 is multiplied by r four times.In the fourth term, the a 1 a 1 is multiplied by r three times ( r In the third term, the a 1 a 1 is multiplied by r two times ( r In the second term, the a 1 a 1 is multiplied by r. The first term, a 1, a 1, is not multiplied by any r. We will then look for a pattern.Īs we look for a pattern in the five terms above, we see that each of the terms starts with a 1. Let’s write the first few terms of the sequence where the first term is a 1 a 1 and the common ratio is r. Can anyone explain to me why the geometric sequence follows the basic structure of an exponential function f (x) a rx and why the arithmetic sequence follows the structure of a linear function f (x) mx + b I get that they are similar concepts but this intrigues me and I would like to understand the reasons behind this similarity. Just as we found a formula for the general term of a sequence and an arithmetic sequence, we can also find a formula for the general term of a geometric sequence. Find the General Term ( nth Term) of a Geometric Sequence Write the first five terms of the sequence where the first term is 6 and the common ratio is r = −4.
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