# RD Sharma Class 11 Chapter 19 Solutions (Arithmetic Progressions)

RD Sharma Solutions for Class 11 Chapter 19 are designed to help you learn and understand all the concepts of arithmetic progressions. In this chapter of RD Sharma Solutions, you will understand what exactly are arithmetic progressions; the sequence, general terms of an arithmetic progression, selections of terms in an arithmetic progression, sums to ‘n’ numbers of arithmetic progressions, properties of arithmetic progressions, insertions of arithmetic means and applications of arithmetic progressions.

Above mentioned topics are comprehensively covered in 7 exercises from exercise 19.1 to 19.7 which have 57 questions. The simplicity of the questions varies from just finding few terms of the sequence of arithmetic progressions to application-based equations.

Instasolv aims to clear all your queries and doubts in this chapter that occur commonly while solving problems of arithmetic progressions. Therefore, you will find all the solutions by your understanding. Also, this will help you understand the logical reasoning of arithmetic progressions, which is very helpful in other exams as well like JEE and NEET.

## Topics Covered in RD Sharma Solutions for Class 11 Chapter 19 – Arithmetic Progressions

**Introduction to Arithmetic Progressions**

A sequence is called an arithmetic progression when the difference between any two successive numbers is the same. For example; 5,6,7,8… is an arithmetic progression because the difference is the same that is 1. Let us take another example; 200, 250, 300… is also an arithmetic progression with the difference between two numbers as 50.

Let us Consider the first term of an arithmetic progression as a0 and the common difference of consecutive numbers as i.

Then, the general form of AP is a_{0},a_{0}+i,a_{0}+2i,a_{0}+3i,…

In general, nth of the sequence is, a_{n}=a_{0}+…. +(n−1)i,

Where i = a_{n} − a_{n-1}.

Example: Consider the sequence 0,2,4,6,8…..

Here, the first term (a_{0}) is 0 and the second number (a_{0}+i) is 2. So, the common difference(i) is,

i= (a_{0}+i)-a0

=2-0

=2

The nth term of the sequence is obtained as follows:

a_{n}=0+(n-2)2

=0+(2n-4)

=2n-4

The nth term of the sequence is a_{n}= 2n−4.

**Sum of Arithmetic series**

The total of an arithmetic series of n terms is observed by making n divided by 2 pairs each with the value of the total of the first and last number. (Try it with the total of the first 10 integers, by making five pairs of 11.)

This gives us the formula: (a+l)

Where a = first term and l = the last term.

As the last term is the nth term = a + (n − 1)i, we can rewrite this as:

[2a+(n-1)d]

Similarly, topics like Finite and Infinite Arithmetic Progression, Properties of Arithmetic Progression, Positive and Negative Common Difference, Representation on Number Line, Graphical Representation of the Arithmetic Progression, Representation on the Cartesian Plane, Arithmetic Series, Formula of the nth term of Arithmetic Series, Arithmetic Mean are explained in these exercises. All the topics have been covered in a manner that students will easily understand and can solve any questions related to them.

## Discussion Exercises of RD Sharma Solutions for Chapter 19 Arithmetic Progressions

- The first exercise, 19.1 of RD Sharma Class 11 Maths Chapter 19 has questions related to basic questions where you have to find terms if you are provided with the nth term or a particular sequence.
- In Exercise 19.2, for the first four questions you are provided with A.P and you have to find its terms or find out if a particular term belongs to the given A.P or not. Further questions get difficult when with the same topic and some sub-topics you get more complex questions.
- The rest of the exercises 19.3-19.7 of chapter 19 covers more complex topics. The mentioned exercises have 57 questions. All the questions are solved in an explicit step-by-step manner, for helping students to interpret the concepts while they solve questions.
- RD Sharma is the best reference book of Maths that is available to date, for all the classes. R D Sharma Class 11 textbooks provide enough questions for each chapter, including many sub-parts. This makes students achieve a proper idea about different types of questions that are asked in the examination as they are in similar terms to the CBSE syllabus.

## Benefits of RD Sharma Solutions for Class 11 Chapter 19 – Arithmetic Progressions by Instasolv

Instasolv provides a customized approach to the topics mentioned in the RD Sharma Class 11 Solutions Chapter 19 of Maths, step by step solutions which makes it easier to understand topics, questions and formulas, which help in school exams and also all the competitive exams that you are preparing for. Our maths experts are constantly working on making basic math concepts easy for you.