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**CBSE NCERT Solutions For Class 10 Maths Chapter 5**: Arithmetic Progression is Chapter 5 of CBSE NCERT Solutions and one of the most important chapters. Students who want to understand the patterns and sequences of arithmetics need to practice the CBSE NCERT Solutions for Class 10 Maths 5. In this article, we have provided the solutions for all the exercises of arithmetic progression for Class 10 students that will give them clarity.

Students can now download the Arithmetic Progression Class 10 PDF designed by experts at Embibe. All the PDF links for the solutions are given in the article below. Practicing the solutions daily can help students score higher marks in the examination.

It is important for students to cover Arithmetic progression for the Class 10 Maths exam. Here we provide the **arithmetic progression Class 10 PDF **for the exercises involved in Chapter 5 for Class 10. The exercises involved in Class 10 Maths NCERT Book Chapter 5 solutions are Exercise 5.1, Exercise 5.2, Exercise 5.3, and Exercise 5.4.

For better preparation, students can download the exercise-wise Class 10 Maths Chapter 5 Arithmetic Progression Solutions from the following table:

Exercise 5.1 | Introduction |

Exercise 5.2 | Arithmetic Progressions |

Exercise 5.3 | Nth Term of an AP |

Exercise 5.4 | Sum of First n Terms of an AP |

The NCERT Solutions for Class 10 Maths Chapter 5 involves Exercise 5.1, Exercise 5.2, Exercise 5.3, and Exercise 5.4. Students can either download the CBSE Solutions PDF for Class 10 Maths Chapter 5 from the link given below or bookmark this page to view the NCERT Solutions when required.

**Q.1. In the given situation, does the list of numbers involved make an arithmetic progression, and why?The taxi fare after each km when the fare is ₹15 for the first km and ₹8 for each additional km.Solution: **From the given data we can see that,

Taxi fare for 1st km =₹15

Taxi fare for first 2 kms=₹(15+8)=₹23 Taxi fare for first 3 kms=₹(23+8)=₹31 Taxi fare for first

4 kms=₹(31+8)=₹39 Clearly, 15,23,31,39…… forms an AP since every term is 8 more than the preceding

term i.e., 23-15=31-23=39-31=8.

Q.2. In the following situation, does the list of numbers involved make an arithmetic progression? If yes, **explain the reason. The amount of air present in a cylinder when a vacuum pump removes 14 of the air remaining in the cylinder at a time.Solution:** Let the initial volume of air in a cylinder be V. In each stroke, the vacuum pump removes 14of air remaining in

the cylinder at a time.

In other words, after every stroke, only 1-14=34 part of air will remain.

Air left in the cylinder after first removal =34V Air again removed =1434V

Air left in the cylinder after second removal =34V-1434V=342V

Air again removed =14342V

Air left in the cylinder after third removal=342V-14342V=343V Therefore, volume of air left in cylinder

follows the sequence: V,34V,342V,343V…. Clearly, the consecutive terms of this sequence do not have

constant difference between them. Thus, this is not an AP.

Download NCERT Solutions for Class 10 Maths Chapter 5

Arithmetic Progression NCERT Solutions provided here are solved by experts of Embibe to help students with their Class 10 board exam preparation. Students can also download the Arithmetic Progression Class 10 NCERT Solutions PDF for offline use.

All the CBSE Class 10 Maths for Class 10 Maths Chapter 5 – Arithmetic Progression comes with detailed, step-by-step solutions. So, with the help of these solutions, students can easily complete their homework and assignments on time and without any difficulty.

**Practice 10th CBSE Exam Questions**

**1st Chapter: Real Numbers****2nd Chapter: Polynomials****4th Chapter: Quadratic Equations****3rd Chapter: Pair Of Linear Equations In Two Variables ****6th Chapter: Triangles****7th Chapter: Coordinate Geometry****8th Chapter: Introduction to Trigonometry****9th Chapter: Some Applications of Trigonometry****10thChapter: Circles****11th Chapter: Constructions****12th Chapter: Areas Related to Circles****13th Chapter: Surface Areas and Volumes****14th Chapter: Statistics****15thChapter: Probability**

**Chapter Description:** An Arithmetic Progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

In this chapter, students will learn the basics of AP – common difference, finite and infinite AP, nth term of an AP, the sum of the first n terms of an AP, etc. Arithmetic Progression can be summarised in the following points:

- An
**Arithmetic Progression**is a sequence of numbers in which the difference between any two successive members is a constant. - When we hear the term ‘progression’, the first thing that comes to our mind is something that changes with time, like increases or decreases with time and position. Arithmetic means that the difference in the value of each subsequent term is constant.
- We also know that the sum of the members of a finite arithmetic progression is called an
**Arithmetic Series.** - In 499 AD, Aryabhata, a prominent mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy gave this method in the
*Aryabhatiya*(section 2.18). - According to an anecdote, young Carl Friedrich Gauss reinvented this method to compute the sum 1+2+3+…+99+100 for punishment in primary school.
- In mathematics, a
**sequence**is a list of objects (or events) that have been ordered in a sequential fashion such that each member either comes before or after, every other member. More formally, a sequence is a function with a domain equal to the set of positive integers. - A
**series**is a sum of a sequence of terms. That is, a series is a list of numbers with additional operations between them.

Check out the benefits of following **NCERT Solutions** by Embibe below:

- All these solutions are illustrated in a detailed manner so that each and every student can understand the concepts easily.
- With the help of these solutions, students can learn the correct approach to solve or answer the questions.
- By using the Chapter 5 NCERT Solutions, Class 10 students can have better clarity of the examination question pattern and marks division. The
**NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.3**and**NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.2**are quite crucial. - Embibe’s NCERT solutions include answers to all the important questions and MCQs given in the NCERT textbook.
- Students can also use these solutions to quickly revise all the concepts before the exams.

**Download** – **Algebra Formulas for Class 10**

Some of the frequently asked questions on Class 10 Maths Chapter 5 are given below:

**Q1. You are given three values, 2x, x + 10, and 3x + 2 which are in AP. Find the value of ‘x’.**

**Ans.** When 2x , x+10, and 3x + 2, the value of x = 6.

**Q3. You are given an AP -5, -10, -15,…, -1000. Find the 10th term of the AP from the end.**

**Ans.** As per the solution, the 10th term of the given AP sequence from the end will be -955.

**Q2. The first term of a given AP is -2, and the common difference between the terms is –2. Find the first four terms.**

**Ans.** According to the given question, the first four terms in a given AP are -2, -4, -6, and **–**8.

**Q4. Name the mathematician who is given the credit of finding the sum of the first 100 natural numbers.**

**Ans.** The name of the mathematician is Carl Friedrich Gauss.

**Q5. The first two terms of a given AP are –3 and 4. Determine the 21st term.**

**Ans.** As per the given question, the 21st term for the AP will be 33.

**Q6. Calculate the value of equation a – 4b + 6c – 4d + e if a, b, c, d, and e are in AP.**

**Ans.** As per the calculation of the given equation, the value of e in the given AP will be 0.

**Q.7. Where can I download the Ch 5 NCERT Solutions Class 10?**

** Ans.** Students can now download the NCERT solutions for Class 10 Maths Chapter 5 PDF from the links given above. These solutions have been designed by academic experts at Embibe aiming to help students score higher marks in the examination.

Now you have been provided with all the necessary information regarding Class 10 Maths Chapter 5 NCERT Solutions – Arithmetic Progression. With these solutions, you can start your preparation and practice questions on Arithmetic Progression.

If you get stuck on a problem, refer to the NCERT Class 10 Solutions for Maths Chapter 5 – Arithmetic Progression. Along with going through these solutions, we also advise you to take Mock Tests on Arithmetic Progression on Embibe for free to improve your knowledge on the topic as well as your time management skills.

At Embibe, you can solve CBSE Class 10 Practice Questions and take Class 10 Mock Tests for free. Along with the solutions and practice questions, you can also refer to and download the NCERT books for Class 10 at Embibe.

**Attempt 10th CBSE Exam Mock Tests**

**Related Links:**

NCERT Solutions For Class 10 Maths (Chapter 4) | NCERT Solutions For Class 10 Maths (Chapter 6) | NCERT Solutions For Class 10 Maths (All Chapters) |

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