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NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4 

 

NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.4 are created by askIITians Maths experts to help you understand all important concepts of the chapter. Practising this exercise will not only solidify your conceptual understanding but will also strengthen your board exam preparation. You can download the NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.4 for free from the askIITians website and study at your own pace. 

 

The fourth exercise of Arithmetic Progressions is a miscellaneous exercise. It is based on all the concepts that you have learned in this chapter. Chapter 5 Arithmetic Progressions of Class 10 Maths helps you understand how arithmetic progressions are formed, how to find the first n terms of an arithmetic progression, and the common difference. In some questions, you have to identify if the given sequences are in the form of an AP or not. It also includes finding the sum of n terms in an arithmetic progression. In some questions, you are given word problems where you have to form the arithmetic progression by yourself and find the required terms. 

 

Let us see how you can download the NCERT Solutions of optional exercise 5.4 of the Arithmetic Progressions chapter. 

About NCERT Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4 

 

Arithmetic Progression: An arithmetic progression or 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.

 

It is given by: a1 , a2 , a3 , . . ., an or a, a + d, a + 2d, a + 3d, . .

 

Common Difference: The fixed number that is added to each term of a list of numbers except the first term to form an AP is called the common difference of the AP. It can be positive, negative or zero. 

 

It is given by: a2 – a1 = a3 – a2 = . . . = an – an – 1 = d, where d is the common difference. 

 

The nth term of an AP: The nth term of the AP with first term a and common difference d is given by an = a + (n – 1) d. 

 

The sum of first n terms of an AP: It is given by the following formula 

 

S = n/2  [2a (n-1)d]

S = n/2  [a +a (n-1)d]

S = n/2  [a +an]

Let an = l 

S = n/2  [a + l]

 

The Sum of n positive integers is given by: 

 

Sn = n(n+1)2

Download Free NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.4 

 

Exercise 5.4 is an optional exercise with 5 unsolved problems. This exercise is not for board exam preparation since it includes advanced-level questions related to Arithmetic Progressions. But, we recommend that you must solve this exercise as it will test how well you understand the concepts of arithmetic progressions. Let us see the different types of questions included in this exercise:

 

Ex 5.4 Q1: In this question, you are given an AP, you have to find its first negative term. 

 

Ex 5.4 Q2: In this question, you are given that the sum of the third and the seventh terms of an AP is 6 and their product is 8. You have to find the sum of the first sixteen terms of the AP.

 

Ex 5.4 Q3: In this question, you are given that a ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are 212m apart, you have to find the length of the wood required for the rungs. 

 

Ex 5.4 Q4: In this question, you are given that the houses of a row are numbered consecutively from 1 to 49. You have to show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. You have to find this value of x.

 

Ex 5.4 Q5: In this question, you are given that a small terrace at a football ground comprises 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of  14 m and a tread of  12 m. You have to calculate the total volume of concrete required to build the terrace. 

 

Key features of NCERT Class 10 Maths Solutions by askIITians: 

  • All the NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.4 are prepared by askIITians experts. 
  • These solutions are based on the latest CBSE syllabus and exam pattern. 
  • You can download the NCERT Solutions for Ex 5.4 for free in PDF form and study at your own pace. 
  • We have included stepwise solutions for all the questions of Ex 5.4 so that you can understand the complete methodology of solving them. 
  • This exercise is preferably suitable for competitive exam preparation so we have included explanatory answers for all questions. 

 

Download NCERT Solutions for all exercises of Class 10 Maths Chapter 5 Arithmetic Progressions: 

 

  • NCERT Chapter 5 Class 10 Maths Ex 5.1 Solutions - 4 Questions
  • NCERT Chapter 5 Class 10 Maths Ex 5.2 Solutions - 20 Questions
  • NCERT Chapter 5 Class 10 Maths Ex 5.3 Solutions - 20 Questions
  • NCERT Chapter 5 Class 10 Maths Ex 5.4 Solutions - 5 Questions

NCERT Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4 FAQs

 

  1. Are the questions of Class 10 Maths Chapter 5 Ex 5.4 asked in board exams? 

No, Ex 5.4 is an optional exercise and the questions mentioned in this exercise are not from board exam perspective. However, we recommend that you must practice all the questions of this exercise since it will help you face all kinds of problems related to arithmetic progressions in the exam. 

 

  1. How to prepare NCERT Class 10 Maths Chapter 5 Ex 5.4 for board exams? 

askIITians provides a plethora of study resources for Arithmetic Progressions such as revision notes, NCERT Solutions, mind maps, daily practice worksheets, extra questions and more. You can use all these study resources to solidify your conceptual understanding of the chapter. 

 

  1. Where can I find online Class 10 Maths coaching? 

You can find the best online coaching for Class 10 Maths at the askIITians website. At akIITians, we provide live interactive classes where students can learn all the concepts of Class 10 Maths from our experts in a classroom-like environment from the safety and comfort of their homes. 







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