NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression | Monster Thinks - Monster Thinks

# NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression

 NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression

NCERT Solutions for Class 10 Maths are solved by experts of MonsterThinks.in in order to help students to obtain excellent marks in their board examination. All the questions and answers in the CBSE NCERT Books have been included in this page. We have provided all the Class 10 Maths NCERT Solutions with a detailed explanation i.e., we have solved all the questions with step-by-step solutions in understandable language. So students having excellent knowledge of NCERT Solutions Class 10 Maths can easily make a grade in their board exams. Read on to find out more about  NCERT Solutions for Class 10 Mathematics.

With the aim of imbibing skills and hard work among the students, the 10th class maths NCERT solutions have been designed. It contains previous years’ questions along with answers except those which are not included in the CBSE 10 maths syllabus.

CBSE NCERT solutions for class 10 maths will help the students acquire good practice to do their CBSE Class 10th exam confidently

## NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression

This article will get the NCERT solutions for Class 10 Mathematics chapter 5 - Arithmetic Progression. All the solutions are framed in a stepwise structure which helps in easily understanding the concepts and formulae applied.

The main topics discussed in Class 10 Mathematics Chapter- Arithmetic Progression are:

• Arithmetic progressions

• nth term of an AP

• Sum of first n terms of an AP.

### Class 10 Maths Arithmetic Progressions Mind Maps

#### Arithmetic Progression (AP)

Consider
(i) 1, 2, 3, 4, ……
(ii) 3, 3, 3, 3, …..
(i) and (ii) are the sequence of numbers, each number in these sequences is called a term.

An arithmetic progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed number ‘d’ to the preceeding term, except the first term.
The fixed number is called the common difference. It can be positive, negative or zero.
Any Arithmetic progression can be represented as :
a, a + d, a + 2d, a + 3d,…..
where ‘a’ is the first term and ‘d’ is the common difference. Arithmetic progressions which does not have a last term are called Infinite Arithmetic Progression. e.g.:
6, 9, 12, 15,…….

#### Formula for common Difference (d)

A sequence of numbers a1, a2, a3…. is an AP if the difference a2 – a1, a3 – a2, a4 – a3…. gives the same value, i.e. if ak+1 – ak is the same for different values of k. The difference (ak+1 – ak) is called common difference (d). Here ak+1 and ak are the (k + 1)th and kth terms respectively.
∴ d = a2 – a1 = a3 – a2 = a4 – a3

#### nth Term (or General Term) of an Arithmetic Progressions

In an AP, with first term ‘a’ and common difference d, the nth term(or the general term) is given by,
an = a + (n – 1)d
Note that an AP can be finite or infinite according to as the number of terms are finite or infinite.
If there are m terms in an AP then am is the last term and is sometimes denoted by ‘l’.

#### Sum of the FIRST ‘n’ Terms of an A.P.

(i) The sum of the first n terms of an A.P. is given by

where a is the first term and d is the common difference
(ii) If l is the last term of the finite A.P. say the nth term, then the sum of all terms of the A.P. is given by,

Note that sum of first n positive integers is given by

#### Arithmetic Mean Between Two Numbers

If a, b, c are in AP. Then b is called the arithmetic mean of a and c and is given by

The questions and answers given in NCERT textbooks at the end of each chapter are not only important for examination but also essential for understanding the concepts in a better way. Hence, we strongly recommend reading these books thoroughly and solving all the exercise questions given at the end of each chapter.

Students searching for the best NCERT Solutions for Class 10 Maths can now get all the solutions from the following link. The solutions by Monster Thinks will help you find a better approach to the questions that follow each chapter of the NCERT textbook.

### Overview of the Exercises Covered in the NCERT Class 10 Maths Chapter 5 Arithmetic Progressions

There are four exercises in chapter 5 on Arithmetic Progressions covered in the syllabus for CBSE Class 10 Term 2. The sums given in each of the four exercises aim to familiarise the students with the concept of arithmetic progressions and their application in various word problems.

Exercise 5.1: The first exercise of NCERT Class 10 Maths Chapter 5 Solutions comprises four sums with several subparts. These sums will familiarise the students with the basic formulas of Arithmetic Progressions, like the formula to find the first and last terms, the formula to calculate the sum of an A.P., and the formula to find an unknown term of an A.P. using the common difference, etc.

Exercise 5.2: The second exercise of NCERT Solutions Class 10 Maths Chapter 5 consists of a total of 20 sums. Several sums covered in this exercise have the application of finding the terms of an A.P. by using formulas and substitution of the known terms of the A.P. There are plenty of word problems in this exercise that will help the students to gain a proper understanding of applying the A.P. formulas.

Exercise 5.3: This exercise comprises a total of 20 sums on arithmetic progressions. Very easy sums to difficult word problems are covered in this exercise. Students are suggested to have a thorough knowledge of all A.P. formulas given in the chapter to solve these sums.

Exercise 5.4: Consists of a total of 5 sums. Students are required to find the first negative term of a given A.P., the first term of a given A.P. from the sum and product of two other known terms of the same A.P., in the first two sums of this exercise. The remaining sums are word problems with a basic application of volume, lengths of objects, etc.