# NCERT Exemplar Class 10 Maths Chapter 5 Solutions: Arithmetic Progression

NCERT Exemplar Class 10 Maths Solutions Chapter 5 ‘Arithmetic Progression’ are written to help you in solving the exemplar exercises. Arithmetic Progressions is a new topic in Class 10 that will develop strong basics for important topics in your higher classes such as progressions. In this chapter of NCERT Class 10 Maths Exemplar, you will get to solve questions related to arithmetic progression and other terms related to it such as common difference, the first term, nth term, and also the sum of all the numbers in a given arithmetic progression. You will also learn the relationship between the nth term of the progression and sum of n terms of the same.

There are 71 questions in this chapter compiled systematically into 4 exercises. You will get to solve a wide variety of questions in this chapter. These NCERT Exemplar problems range from beginner level questions to advanced level. There are MCQs, short answer types and long answer questions that can be asked in your exams. These questions will help you learn time management skills and will also aid you in quick revision before your exams.

Instasolv has provided the answer to each and every math problem in a detailed manner. You will find the language used by the Instasolv maths faculty very simple to understand. It is highly recommended that you use the solutions provided here as your source of reference.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 5: Arithmetic Progression

**Introduction to Arithmetic Progression (AP)**

There are various types of series and progressions that we come across in our daily lives, the successive value of which may be obtained by multiplying a common number or adding a common difference or by other methods.

In arithmetic progression, every successive term of the progression is evaluated by adding a number d to the previous number. This d is also termed as a common difference.

The common difference in an arithmetic progression can be negative, positive or zero.

The common notations used are ‘a’ for the first term, a_{n} for nth term, and d for the common difference.

**General Form of an AP**

a, a+2d, a+3d…is the general form of an AP.

**n****th Term of an AP**

The nth term for a given an AP with common difference d and first term a is given such that,

a_{n}=a+(n-1)d

a_{n} is the notation for a general term while a_{m} or l denotes the last term of the AP.

**Sum of first n terms of an AP**

It is denoted by S_{n} and is given such that,

S_{n}=n[2a+(n-1)d]/2

Also, S=n(a+l)/2

The sum of first n positive integers can be given as,

S=n(n+1)/2

The nth term of an arithmetic progression can also be given as the difference between the sum of n terms and sum of (n-1) terms of the same, that is,

a_{n}=S_{n}-S_{n-1}

### Exercise Discussion for NCERT Exemplar Class 10 Maths Solutions Chapter 5: Arithmetic Progression

- The exercises in this chapter comprehensively cover all the possible types of questions that can be asked in CBSE Class 10 exams. You will get to solve numerical math problems as well as statement-based problems in the Exemplar exercises.
- Exercise 5.1 comprises a number of multiple-choice questions in an increasing level of difficulty on topics such as finding the first-two terms of AP, finding the common difference, finding the nth term of an AP, etc.
- Exercise 5.2 consists of a broad range of short answer type questions where you have to find if the given patterns are in AP or not. These questions are very scoring if you grasp the core concept of the topics.
- The third exercise 5.3 is based on conceptual and practical math problems which are mostly statement based. You have to verify if the given numbers are in AP and hence find the next three terms.
- You will get many long answer questions in the final exercise 5.4 on topics such as the sum of n terms of an arithmetic progression, finding the AP when the sums of its first three terms and the last three terms are given to you, etc.

**Why use NCERT Exemplar Class 10 Maths Solutions Chapter 5: Arithmetic Progression by Instasolv?**

- Solving the NCERT Class 10 Exemplar Problems for Maths Chapter 5 by using the solutions by Instasolv will enhance your exam score substantially.
- These solutions for NCERT Exemplar at Instasolv are written in a step by step format with reasons mentioned alongside every step.
- You will find consistency in the quality of answers provided by the expert team of Instasolv.
- At Instasolv, you will learn to approach a question related to an arithmetic progression in the right manner, which will help you rank considerably good in competitive exams of your level.
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