![]() ![]() Ĭ) Find r given that a 1 = 10 and a 20 = 10 -18ĭ) write the rational number 0.9717171. S = a 1 / (1 - r) = 0.31 / (1 - 0.01) = 0.31 / 0.99 = 31 / 99Īnswer the following questions related to geometric sequences:Ī) Find a 20 given that a 3 = 1/2 and a 5 = 8ī) Find a 30 given that the first few terms of a geometric sequence are given by -2, 1, -1/2, 1/4. Hence the use of the formula for an infinite sum of a geometric sequence are those of a geometric sequence with a 1 = 0.31 and r = 0.01. We first write the given rational number as an infinite sum as followsĥ.313131. ![]() 7) a Find the missing term or terms in each geometric sequence. 5) a Given two terms in a geometric sequence find the common ratio, the explicit formula, and therecursive formula. = 8 × (1 - (1/4) 10) / (1 - 1/4) = 10.67 (rounded to 2 decimal places) Given the explicit formula for a geometric sequence find the common ratio, the term named inthe problem, and the recursive formula. ![]() These are the terms of a geometric sequence with a 1 = 8 and r = 1/4 and therefore we can use the formula for the sum of the terms of a geometric sequence a_n = a_1 \dfracĪn examination of the terms included in the sum areĨ, 8× ((1/4) 1, 8×((1/4) 2. The sum of the first n terms of a geometric sequence is given by Where a 1 is the first term of the sequence and r is the common ratio which is equal to 4 in the above example. ![]() The terms in the sequence may also be written as follows 2 is the first term of the sequence and 4 is the common ratio. Has been obtained starting from 2 and multiplying each term by 4. Problems and exercises involving geometric sequences, along with answers are presented. Geometric sequences are used in several branches of applied mathematics to engineering, sciences, computer sciences, biology, finance. Geometric Sequences Problems with Solutions Geometric Sequences Problems with Solutions 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.
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