# Progression

## Overview

Welcome to the comprehensive course material on Progressions in Algebra. Progressions are sequences of numbers that follow a specific pattern or rule. In this topic, we will delve into various types of progressions, including Arithmetic Progression (A.P.) and Geometric Progression (G.P.), their properties, and how to compute their terms and sums efficiently.

Arithmetic Progression (A.P.): An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. For instance, 2, 5, 8, 11, 14 is an arithmetic progression with a common difference of 3. We will explore how to determine the nth term of an arithmetic progression and calculate the sum of the terms in an arithmetic progression efficiently.

Geometric Progression (G.P.): In a geometric progression, each term after the first is found by multiplying the preceding term by a fixed, non-zero number called the common ratio. For example, 2, 6, 18, 54, 162 is a geometric progression with a common ratio of 3. We will discuss how to find the nth term of a geometric progression and compute the sum of the terms up to a certain point or to infinity.

In the study of progressions, it is essential to understand the formulas used to calculate the nth term and the sum of terms in both arithmetic and geometric progressions. These formulas provide a systematic approach to solving problems related to progressions efficiently and accurately.

Furthermore, we will explore scenarios where the sum of an infinite number of terms in a geometric progression converges to a specific value. Understanding the convergence properties of geometric progressions is crucial in various mathematical and real-world applications.

Summing Up: Progressions play a vital role in mathematics and have diverse applications in different fields such as finance, physics, and computer science. By mastering the concepts of arithmetic and geometric progressions, you will not only enhance your problem-solving skills but also develop a deeper understanding of mathematical patterns and sequences.

Get ready to embark on a journey through the fascinating world of progressions, where you will uncover the beauty and utility of these mathematical sequences.

## Objectives

1. Compute The Sum Of A P And GP
2. Find The Sum To Infinity Of A Given GP
3. Determine The Nth Term Of A Progression

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## Lesson Evaluation

Congratulations on completing the lesson on Progression. 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.

1. What is the nth term of the arithmetic progression: 5, 9, 13, 17, ...? A. 4n + 1 B. 5n - 1 C. 4n + 5 D. 5n + 1 Answer: A. 4n + 1
2. Find the sum of the arithmetic progression: 2, 5, 8, 11, ... up to the 10th term. A. 95 B. 102 C. 110 D. 118 Answer: B. 102
3. Determine the common ratio of the geometric progression: 3, 9, 27, 81, ... A. 3 B. 6 C. 9 D. 12 Answer: A. 3
4. Calculate the sum to infinity of the geometric progression: 4, 12, 36, 108, ... A. 144 B. 216 C. 288 D. Infinity Answer: D. Infinity
5. What is the 8th term of the geometric progression: 2, 6, 18, 54, ...? A. 4374 B. 729 C. 328 D. 162 Answer: B. 729
6. Compute the sum of the arithmetic progression: 3, 7, 11, 15, ... up to the 20th term. A. 380 B. 400 C. 420 D. 440 Answer: C. 420
7. Find the next term in the sequence: 1, 4, 9, 16, ... A. 25 B. 36 C. 49 D. 64 Answer: B. 36
8. Calculate the sum to infinity of the geometric progression: 10, 5, 5/2, 5/4, ... A. 20 B. 10 C. 5 D. 2.5 Answer: A. 20
9. What is the 5th term of the arithmetic progression: 12, 18, 24, 30, ...? A. 38 B. 42 C. 36 D. 48 Answer: B. 42

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Progression from previous years

Question 1

What is the general term of the sequence 3, 8, 13, 18, ...?

Question 1

Which of the following could be the inequality illustrated in the sketch graph above?

Question 1

T varies inversely as the square root of F when T = 7, F = 2$$\frac{1}{4}$$. Find T when F = $$\frac{27}{9}$$

Practice a number of Progression past questions