Geometric sequence3/2/2023 ![]() R=√2 r= the number you times by to get to the next term a= 2 √2 a= the first term of the sequence What terms have you got/need to find? the 10th term nth term = arn-1 1 2 3 4. ![]() r= the number you times by to get to the next term a= the first term of the sequence What terms have you got/need to find? So what do we have: 1 2 3 4 ?, 4, ?, 8. Find the values of a) the common ration b) first term and c) the 10th term. The second term of a geometric sequence is 4 and the 4th term is 8. R= the number you times by to get to the next term Your check list You will need to find or use these: a= the first term of the sequence What terms have you got/need to find? The second term of a geometric sequence is 4 and the 4th term is 8. r= 5 a=2 ar ar2 ar3 arn-1 a This is the same for all geometric sequences How do we find the nth term? r= the number you times by to get to the next term a= the first term of the sequence 1 2 3 4 n Eg2, 10, 50, 250. r= x x x = 10 10 = -30 -30= 90 Common ratio =u2 u1 ‘Second term divided by the first’ This number is called the common ratio, r. Geometric Sequence A geometric sequence is one where to get from one term to the next you multiply by the same number each time. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. 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 Multiplying any term of the sequence by the common ratio 6 generates the subsequent term. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. The yearly salary values described form a geometric sequence because they change by a constant factor each year. ![]() ![]() In this section, we will review sequences that grow in this way. When a salary increases by a constant rate each year, the salary grows by a constant factor. His salary will be $26,520 after one year $27,050.40 after two years $27,591.41 after three years and so on. His annual salary in any given year can be found by multiplying his salary from the previous year by 102%. He is promised a 2% cost of living increase each year. Suppose, for example, a recent college graduate finds a position as a sales manager earning an annual salary of $26,000. Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation. Use an explicit formula for a geometric sequence.Use a recursive formula for a geometric sequence. ![]() List the terms of a geometric sequence.Find the common ratio for a geometric sequence. ![]()
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