Arithmetic And Geometric Series
Overview
Sequences appear everywhere: in savings accounts earning compound interest, in the spacing of fence posts, in the decay of radioactive atoms. Recognising whether a sequence is arithmetic or geometric unlocks powerful formulas that let you jump straight to the 100th term or add a thousand terms in a single calculation, without writing them all out.
This topic equips you with the general-term and summation formulas for both types of series. You will learn to handle finite sums, discover when an infinite geometric series converges, and master the techniques examiners reward in the 4PM1 papers. Every formula is derived so you understand where it comes from, not just how to use it.
Objectives
- Know the general term of an arithmetic series
- Use the sum to n terms of an arithmetic series
- Know the general term of a geometric series
- Use the sum to n terms of a finite geometric series
- Use the sum to infinity of a convergent geometric series, including the use of |r| < 1
Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Arithmetic And Geometric Series. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- The 10th term of the arithmetic sequence 3, 7, 11, 15, ... is: A) 39 B) 43 C) 35 D) 37 Answer: A
- A geometric sequence has first term 5 and common ratio -2. What is the 4th term? A) -40 B) 40 C) -80 D) 16 Answer: A
- Which condition must be satisfied for a geometric series to have a sum to infinity? A) r > 1 B) r < 1 C) |r| < 1 D) |r| > 1 Answer: C
- The sum of the first 20 terms of the arithmetic series 2 + 5 + 8 + 11 + ... is: A) 590 B) 610 C) 570 D) 620 Answer: B
- A geometric series has first term 10 and sum to infinity 40. The common ratio is: A) 1/4 B) 3/4 C) 1/2 D) 2/5 Answer: B
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Practice Mock Questions
Want to practice mock questions on Arithmetic And Geometric Series? Download the Green Bridge CBT app to access mock questions and full practice assessments for this topic.
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