Pressing the right or left arrows will change the value of A and updates the graph each time. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Step 1 For the first part of this activity, students explore geometric sequences graphically by varying the value of A, the common ratio. In contrast, a geometric sequence is one where each term equals the one before it multiplied by a certain value. Each term in this sequence equals the term before it with 5 added on. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis An arithmetic series is one where each term is equal the one before it plus some number. 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 The twelfth term of the sequence is 0, a 12 = 0. They gave me five terms, so the sixth term of the sequence is going to be the very next term. Ī n = a 1 + ( n − 1 ) d a n = a 1 + ( n − 1 ) dġ0 = a 1 + ( 7 − 1 ) ( −2 ) 10 = a 1 + ( 7 − 1 ) ( −2 )ġ0 = a 1 + ( 6 ) ( −2 ) 10 = a 1 + ( 6 ) ( −2 )įind the twelfth term, a 12, a 12, using theįormula with a 1 = 22, n = 12, and d = −2. Well construct arithmetic and geometric sequences to describe patterns and use. The difference is always 8, so the common difference is d 8. To first find the first term, a 1, a 1, use theįormula with a 7 = 10, n = 7, and d = −2.
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