Higher Algebra Hall & Knight Arithmetical Progression (Chapter 4) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 4: Arithmetic Progression will help you prepare for Class 12 Maths exams along with competitive exams like JEE and NEET. Arithmetic Progression in Hall & Knight Algebra Book comprises of all the imperative concepts that are required to understand arithmetic series, fundamental formula and insertion of the arithmetic mean. You will also learn about the concepts of progression and common difference from the chapter. The concepts have been dealt to ensure that you are prepared for your competitive exams along with your regular exams. 

Chapter 4: Arithmetic Progression of Higher Algebra by Hall and Knight book with solutions has 2 exercises which have 50 unsolved questions. Once you solve these questions you will get used to tackling these problems which deal with number series, unknown quantities, arithmetic progressions and common differences. This exercise is an overall blend of all the foundation concepts that have been dealt in the chapter and presents a very engaging approach for the revision and practice of those concepts for complete JEE Advanced preparation. 

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Important Topics for Hall and Knight Higher Algebra Solutions Chapter 4: Arithmetic Progression

Arithmetic Progression 

As the name of the chapter suggests, this is the core concept around which all the other topics of the chapter revolve. In this chapter, you will be introduced to arithmetic progression and you will learn that whenever quantities tend to increase or decrease by a common difference, such that they form a series, they are termed as arithmetic progressions. These arithmetic progressions can be of integers, variables, fractions or even cubes and roots. They can have positive or negative or both kinds of values. 

For example 

2, 5, 8, 11,……..

a, a + b, a + 2b, a + 3b,………

8, 2, -4, -10………

All these three series discussed above have similar intervals and form a series, therefore they qualify to be arithmetic progressions. 

Addition and subtraction of Arithmetic Progressions 

In this chapter, now that you are familiar with the idea of arithmetic progressions, you will learn to perform mathematical operations like addition and subtraction on them. 

The chapter deals with specific steps and formulas which are applied on the given series of progressions to derive their added value or their difference. Along with adding the terms of a single given arithmetic progression, you will also learn to add two different series together or subtract two different series. 

These fundamentals of performing arithmetic operations will be used when you will have to find a certain number of term, for example, the 57th term of a given series. 

Arithmetic mean 

This is a very important term which you will encounter in the chapter and which will help you solve the problems related to series and the different scenarios of problems which you will encounter. 

In case if a series has three quantities in it, then the quantity which will be in the middle, will be termed as the arithmetic mean. 

Similarly, in case of long series, the middle-value id considered to be the arithmetic mean. You will encounter questions from the chapter, where you will be provided with the arithmetic mean and you will have to use it to find the series or the first and last term of it. 

Exercise-wise Discussion of Hall & Knight Higher Algebra Solutions Chapter 4: Arithmetic Progression

Examples IV.a 

  • The exercise of the chapter begins with 26 questions. 
  • The first-few questions are very easy as they deal with finding the sum of the given series up to  a certain number of given terms
  • Then, there are questions where you are required to find the sum of the given series till n terms.
  • Some of the questions deal with fractional quantities, cubes, cube roots, and negative integers as well. 
  • From question number 13 to 16, there are problems where you are required to insert a certain number between the given extremes of a series. 
  • You are required to use the concept of arithmetic progression in these questions in order to find the nth terms and a certain given number of values. 
  • The exercise also has many word problems and logical questions which are very important from the perspective of competitive exams. 

Example IV.b 

  • The second exercise consists of a total of 24 questions.
  • The exercise begins with simple analytical problems where you are required to find the number of terms that are required to make a certain mentioned value. 
  • There are questions wherewith the given amount of information you are required you find the first term of the series 
  • There are questions which work on the formula of n as a part of the deriving arithmetic sum of the given fractional terms.
  • The exercise consists of problems where you are required to prove whether the given progression is even or not
  • There are many more condition-based word problems in the exercise. 

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