NCERT Solutions Class 10 Maths Chapter 5 guides you through Arithmetic Progressions with step-by-step solutions to all 49 questions. You’ll learn how to find the nth term using the formula an = a + (n-1)d, calculate the sum of AP series using Sn = n/2[2a + (n-1)d], and solve real-world problems involving sequences. Master techniques to identify common differences, determine missing terms, and apply AP formulas in word problems that frequently appear in CBSE board exams.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 5 Arithmetic Progressions – Complete Guide
NCERT Class 10 Chapter 5 on Arithmetic Progressions introduces you to one of the most important sequence patterns in mathematics. You’ll explore how AP appears everywhere—from stacking chairs to calculating savings, from construction planning to time-based calculations. This chapter builds a strong foundation for understanding patterns and sequences that you’ll encounter in higher mathematics and competitive examinations.
📊 CBSE Class 10 Maths Chapter 5 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 5 Marks |
| Unit Name | Algebra |
| Difficulty Level | Medium |
| Importance | Medium |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 1-2 questions |
In this chapter, you’ll learn to identify arithmetic progressions, find the common difference, and determine any term in the sequence using the nth term formula. You’ll also master the derivation and application of formulas for finding the sum of first n terms of an AP. The chapter includes both theoretical concepts and practical problem-solving techniques that are crucial for CBSE board examinations, where this topic typically carries 5 marks through a mix of MCQs, short answer questions (2-3 marks), and one long answer question (4 marks).
The beauty of Arithmetic Progressions lies in their predictability and wide applications. You’ll discover how AP concepts connect with real-life situations like calculating monthly savings, determining seating arrangements, analyzing linear growth patterns, and solving problems related to time and distance. The chapter also strengthens your algebraic skills as you work with formulas and solve equations involving AP terms.
Quick Facts – Class 10 Chapter 5
| 📖 Chapter Number | Chapter 5 |
| 📚 Chapter Name | Arithmetic Progressions |
| ✏️ Total Exercises | 4 Exercises |
| ❓ Total Questions | 49 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Arithmetic Progressions is essential not just for scoring well in your CBSE Class 10 board exams, but also for building analytical thinking skills. The step-by-step NCERT solutions help you understand each concept thoroughly, from basic identification of AP to complex problem-solving involving multiple conditions. With consistent practice of the exercise questions and previous year board problems, you’ll gain confidence in tackling any AP-related question efficiently and accurately.
NCERT Solutions Class 10 Maths Chapter 5 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 5.1 | Complete step-by-step solutions for 4 questions | 📥 Download PDF |
| Exercise 5.2 | Complete step-by-step solutions for 20 questions | 📥 Download PDF |
| Exercise 5.3 | Complete step-by-step solutions for 20 questions | 📥 Download PDF |
| Exercise 5.4 (Optional) | Complete step-by-step solutions for 5 questions | 📥 Download PDF |
Arithmetic Progressions – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| nth term of an AP \(a_n = a + (n-1)d\) | Finds the nth term of an arithmetic progression (AP) Note: a is the first term, d is the common difference, and n is the term number. Remember to subtract 1 from ‘n’ before multiplying by ‘d’. | When you need to find a specific term in an AP, given the first term, common difference, and term number. |
| Common Difference \(d = a_2 – a_1\) | Calculates the common difference of an AP Note: Subtract any term from its succeeding term to find the common difference. Make sure the difference is constant for the sequence to be an AP. | When you need to find the difference between consecutive terms in a sequence to check if it’s an AP or to use in other formulas. |
| Sum of first n terms of an AP \(S_n = \frac{n}{2}[2a + (n-1)d]\) | Calculates the sum of the first n terms of an AP. Note: This formula is useful when you know the first term and common difference. Remember the order of operations (PEMDAS/BODMAS). | When you need to find the total sum of a certain number of terms in an AP, given the first term, common difference, and number of terms. |
| Sum of first n terms (alternative) \(S_n = \frac{n}{2}(a + a_n)\) | Calculates the sum of the first n terms of an AP (using the last term). Note: Here, a_n is the last term (nth term). This is a shorter formula when you already know the last term. | When you know the first term and the last term of the AP, and the number of terms. |
| nth term from the end \(a_n’ = l – (n-1)d\) | Finds the nth term from the end of an AP Note: l is the last term of the AP. Be careful to distinguish between ‘n’ from the beginning and ‘n’ from the end. | When the question asks for a term counting from the last term of the AP. |
| Finding n when Sn is given \(S_n = \frac{n}{2}[2a + (n-1)d]\) (Solve the quadratic) | Finding number of terms ‘n’ when the sum Sn is given Note: Solve the resulting quadratic equation for ‘n’. Discard any negative or fractional solutions, as ‘n’ must be a positive integer. | When the problem provides the sum of ‘n’ terms and asks for ‘n’. This often leads to a quadratic equation. |
| Arithmetic Mean \(A = \frac{a+b}{2}\) | Calculates the arithmetic mean (average) of two numbers a and b Note: This is also the average of the two numbers. ‘A’ is the arithmetic mean between ‘a’ and ‘b’. | When you need to insert a single number between two given numbers to make an AP. |
| Relationship between Sn and an \(a_n = S_n – S_{n-1}\) | Finds the nth term using the sum of the first n terms and the sum of the first (n-1) terms. Note: This is useful when you don’t know the first term and common difference directly. | When you are given the formulas or values of Sn and S(n-1) and need to find a specific term. |
| Sum of first n natural numbers \(S_n = \frac{n(n+1)}{2}\) | Calculates the sum of the first n natural numbers (1 + 2 + 3 + … + n) Note: This is a special case of an AP where a = 1 and d = 1. | When you need to find the sum of a sequence of consecutive natural numbers starting from 1. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 5
📚 Related Study Materials – Class 10 Maths Resources
| Resource | Access |
|---|---|
| NCERT Class 10 Maths All Chapters | View Solutions |
| NCERT Class 10 Science Solutions | View Solutions |
| NCERT Class 10 Social Science | View Solutions |
| NCERT Class 10 English Solutions | View Solutions |