# NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions

NCERT solutions for class 10 Maths Chapter 5 – Arithmetic Progressions have been drafted by expert Maths teachers. NCERT Class 10 Maths Chapter 5 solutions have been created following the latest guidelines given in CBSE approved Class 10 Maths syllabus. NCERT Solutions CBSE Class 10 Maths Chapter 5 comprises 49 unsolved questions that cover different topics from the chapter. Some of the important topics covered in this chapter include an introduction to arithmetic progression, nth term of an arithmetic progression, and the sum of first nth terms of an arithmetic progression.

Arithmetic Progressions contain answers to all the questions asked in this chapter in detail. Our methodical solutions help you to develop an in-depth understanding of all the topics covered in Chapter 5. Questions given in Class 10 Maths Arithmetic Progressions are solved in such a manner that they make the process of learning interesting and interactive.

Arithmetic Progressions helps to lay down the right conceptual foundation for higher-level classes. This will help you to gain the confidence to ace the board exams and various competitive exams in future. The questions have been solved using the best methods of solving the problems and will give you enough practice to become thorough with all important concepts. They clear your doubts and guide you to excel in your class 10^{th} board exams.

## NCERT Class 10 Maths Chapter 5 – Class 10 Maths Arithmetic Progressions

**Introduction**

This part of the Class 10 Maths Arithmetic Progressions chapter introduces you to the daily life patterns, in which succeeding terms are obtained by adding a fixed number to the preceding terms. It also tells you how we can find nth terms and the sum of n consecutive terms and use this knowledge to solve some daily life problems.

**Arithmetic Progressions**

This section of CBSE NCERT Solutions for Class 10 for Maths Chapter 5 tells you that each entry in a list of numbers is called a term. An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. This fixed number is called the common difference of the AP, and it can be positive, negative or zero. The general form of an AP can be given as –

a, a + d, a + 2d, a + 3d, . . .

where a is the first term and d the common difference.

If there are a finite number of terms in AP, it is called a finite AP, and it has the last term. The AP which doesn’t have the last term is known as infinite Arithmetic Progression.

In general, for an AP a* _{1}*, a

*, . . ., an, we have d = a*

_{2}*+ 1 – a*

_{k}*where a*

_{k}*+ 1 and a*

_{k}*are the (k + 1)*

_{k}*and the kth terms respectively. So, a given list of numbers a1, a*

_{th}*, a*

_{2}*, . . . is called an AP, if the differences a*

_{3}*– a*

_{2}*, a*

_{1}*– a*

_{3}*, a*

_{2}*– a*

_{4}*, . . ., give the same value (i.e., if a*

_{3}*+ 1 – a*

_{k}*is the same for different values of k).*

_{k}**The nth term of an AP**

In an AP with first term a and common difference d, the *n*th term (or the general term) is given by an = a + (*n* – 1) d. Here, an is also called the general term of the AP. If there are *m* terms in the AP, then a* _{m}* represents the last term which is sometimes also denoted by

*l*.

**Sum of First***n*Terms of an AP

In our NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions you will learn that The sum of the first *n* terms of an AP is given by:

S = n/2 [2a + (n-1) d]

If *l* is the last term of the finite AP, say the *n*th term, then the sum of all terms of the AP is given by

S = n/2 (a + *l*]

We use S* _{n}* in place of S to denote the sum of first

*n*terms of the AP.

### NCERT Class 10 Maths Chapter 5 – Arithmetic Progressions Exercises

In this chapter of CBSE NCERT 10 Maths Book, there are total 4 exercises NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions answer all the 49 questions given in 4 exercises in a step by step manner to help you understand complex topics easily. The components of the exercises are discussed below.

**Exercise 5.1**

This exercise contains 4 questions. Question 1 asks you to identify if the given lists are arithmetic progressions or not. Questions 2, 3 and 4 are based on finding the first term and the common difference of the given AP.

**Exercise 5.2 **

This exercise contains 20 questions. Questions 1 to 6 asks you to find the missing terms when a (the first term), d (common difference) and a* _{n}* (

*n*th term) of the AP are given. Questions 7 to 11 and 17 ask you to find out some specific terms in case of the given APs. Questions 12 to 16 and 18 to 20 give you some situations which you need to convert to suitable AP.

**Exercise 5.3 **

This exercise contains 20 questions. Question 1 to 4 asks you to calculate the sum of APs given. Questions 5 to 14 either ask you to find the sum of terms or number of terms/common difference provided the sum of terms is given. In questions 15 to 20, the given word problems are to be converted to valid APs, and related values are to be determined. This last set of questions utilizes your analytical and application skills.

**Exercise 5.4 **

This exercise contains 5 questions. All the questions from this exercise are word problems and utilize your higher-order thinking skills to convert the given situations to APs and solve them for required queries related to the concepts learnt in the chapter.

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions have been efficiently prepared by using the best techniques of solving AP questions.