# Higher Algebra Hall & Knight Geometrical Progression (Chapter 5) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 5 ‘Geometrical Progression’ provides an insight into the topics that will help you in easy exam preparation. These solutions would help in developing a better understanding of the basic concept of progression along with the insertion of geometric means, the sum of n terms of a geometrical series, and the sum of infinite geometrical series. The chapter also covers basic ideas of the rule of reduction, reduction of recurring decimals, the sum of n terms of series and sum of n terms of arithmetic-geometric series. You will also learn about the concepts of common ratio, insertion of geometric means and preceding value from the chapter.

Higher Algebra by Hall and Knight ‘Geometric Progression’ solutions include 2 exercises with 51 questions. These exercises contain all the diverse topics that have been covered in the chapter and the different kinds of questions which can be formulated for IIT JEE as well as Class 12 board exams. Once you solve these questions you will learn to tackle problems which deal common ratio, geometric progression, geometric mean and insertion of mean between a series.

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## Important Topics for Hall and Knight Higher Algebra Solutions Chapter 5: Geometric Progression

**Geometric Progression**

As the name of this chapter suggests, in this chapter, you will be introduced to the concept of Geometric progression. When quantities tend to experience an increase or a decrease in their value by a factor which is constant in nature, the quantities are termed to be of geometric progression.

You will also get to learn that the constant factor of increase or decrease in the quantities is also termed as the common ratio. This common ratio plays a very essential role in determining a geometric progression and this common factor can be found by dividing any of the terms by the term which precedes it immediately.

Considering a very simple example, if we analyse the following series ‘a, ac, acc, acccc…’ we can easily figure out that the difference amongst each preceding term is of “c” therefore in this example “c” is the common ratio.

**Geometric Mean **

When we consider three quantities which qualify for being a part of a series which is in progression, the quantity that remains in the centre is termed as the geometric mean between the other two quantities.

In this chapter of Higher Algebra by Hall & Knight, you will learn the ways of finding the geometric means and you will come across different questions where this mean will be inserted between certain values of the given series to derive answers.

There are questions regarding the insertion of geometric means between two given quantities and the use of mean to find the sum of the series. The chapter has a detailed explanation of all the steps and fundamentals required to solve such questions and make adequate use of the geometric mean.

### Exercise Discussions of Hall and Knight Higher Algebra Chapter 5: Geometric Progression

**Examples Va **

**The first exercise of the chapter comprises of 28 questions.**

**Most of the questions included in this exercise belong to the types which have been dealt with in the solved example portions with detailed explanations.**

- It begins with the basic questions where you are required to add up the given series to the particular number of terms that have been mentioned in the question.

- Some of these questions contain variable limits like “2n” and “p”

- Then there are questions where you are required to insert the geometric mean between the given extremes of a series.

- There are questions where you are required to sum up the series up to infinity

- The last portion of the exercise consists of word problems which deal with recurring decimals, common ratio, insertion of means and some proving questions.

**Example V b **

**This exercise contains a total of 23 questions which are solved by deriving the product of the corresponding terms.**

**The exercise begins with questions where you are required to derive the sum of the given series till either “n” terms or till infinity.**

- The exercise contains fraction based questions as well

- There are questions where you are required to prove the given conditions of a geometric progression

- There are word problems based on arithmetic mean, common ratio, the first term of the series, last term of the series, a positive integer, and indefinitely small values.

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