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Geometric series problems. Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given. See full list on analyzemath. . Scroll down the page for more examples and solutions of geometric series. 2 The first two terms of a geometric sequence and an arithmetic sequence are the same. Solve ten (10) questions and verify your solutions by comparing them with the provided answers. Problem 10: Calculate the sum of the first 10 terms of the harmonic series. Nov 16, 2022 · Here is a set of practice problems to accompany the Series and Sequences chapter of the notes for Paul Dawkins Calculus II course at Lamar University. Jul 23, 2025 · A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Kindly mail your feedback to v4formath@gmail. The ratio between consecutive terms in a geometric Learning Objectives By the end of this section, you will be able to: Determine if a sequence is geometric Find the general term (\ (n\)th term) of a geometric sequence Find the sum of the first \ (n\) terms of a geometric sequence Find the sum of an infinite geometric series Apply geometric sequences and series in the real world 4. The first term is 12. A sequence is called a geometric sequence if the ratio between consecutive terms is always the same. com We always appreciate your feedback. Sharpen your math proficiency with these Geometric Series Practice Problems. To see that the series does not converge absolutely, it suffices to show that the series ∞ ∞ X 1 Example 1: Determine the sum of the first 10 terms of each geometric sequence: 4 + 12 + 36 + ⋯ 1 = 5, 1 = 2 The following diagrams give the formulas for the partial sum of the first nth terms of a geometric series and the sum of an infinite geometric series. The sum of the first three terms of the geometric sequence is 3 more than the sum of the first three terms of the arithmetic sequence. com converge absolutely, converge conditionally, or diverge? Answer: The terms √ 1 are decreasing and go to zero (you should check this), so the Alternating n2+1 Series Test says that the series converges. Jul 23, 2025 · Problem 9: Determine the sum of an infinite geometric series where the first term a1 is 9 and the common ratio r is 1/3 . ywdo cpqfqgit xaqjd qdhw abry benufoq pmadlq iehdh yjxiwl qlcg