NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions
Students searching for accurate and easy-to-follow NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions will find everything they need at Myclass24. Arithmetic Progressions, commonly known as AP, is one of the most rewarding chapters in Class 10 Maths because the formulas are few but the application range is wide. Once students understand the structure of an AP — the first term (a), the common difference (d), and the nth term (aₙ) — solving even complex problems becomes straightforward. Myclass24's solutions cover all four exercises of Chapter 5 with detailed workings and exam-focused explanations.
Whether it's finding the sum of the first 20 terms or determining whether a given list of numbers forms an AP, the solutions are laid out step-by-step for maximum clarity. Chapter 5 also features some of the most interesting word problems in the entire Class 10 Maths book, including problems on savings, stacking, seating arrangements, and even sports applications. These make the chapter both practically relevant and exam-scoring.
Download PDF – NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions
The PDF of NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions is freely available on Myclass24. It covers Exercise 5.1, Exercise 5.2, Exercise 5.3, and Exercise 5.4 (optional). The PDF is formatted to be mobile-friendly, with clear formulas and step-wise solutions that load well on smartphones and tablets.
Chapter 5 Arithmetic Progressions – Core Formulas, Facts & Exercise Breakdown
NCERT Class 10 Arithmetic Progression is a list of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference (d). If the first term is a and the common difference is d, then the nth term of the AP is given by: aₙ = a + (n–1)d. This formula allows finding any term of an AP directly without listing all previous terms. The sum of the first n terms is given by: Sₙ = n/2 [2a + (n–1)d] or alternatively Sₙ = n/2 (a + l), where l is the last term. A critical relationship is aₙ = Sₙ – Sₙ₋₁, which means the nth term equals the difference of the sum of n terms and sum of (n-1) terms. This identity appears in many tricky CBSE problems.
| Exercise | Topics Covered | No. of Questions | Difficulty Level |
| Exercise 5.1 | Introduction to AP, identifying AP from list | 4 | Easy |
| Exercise 5.2 | nth Term Formula (aₙ = a + (n–1)d) | 20 | Easy–Medium |
| Exercise 5.3 | Sum of n Terms (Sₙ formula) | 20 | Medium–Hard |
| Exercise 5.4 | Optional – Higher-Order AP Problems | 5 | Hard |
| Formula | Expression | Used For |
| nth Term | aₙ = a + (n–1)d | Finding any specific term |
| Sum of n Terms (Form 1) | Sₙ = n/2 [2a + (n–1)d] | When first term & d are known |
| Sum of n Terms (Form 2) | Sₙ = n/2 (a + l) | When first & last term are known |
| Common Difference | d = aₙ – aₙ₋₁ | Verifying AP; finding d |
| Number of Terms | n = (l – a)/d + 1 | Finding total terms in a finite AP |
| Middle Term (odd n) | a(n+1)/2 | Middle term of finite AP |
One fact that surprises many students: if three numbers a, b, c are in AP, then 2b = a + c. This simple property is used in problems where you are asked to find three or four numbers in AP given their sum and product. Another frequently tested concept is finding the sum of the first n natural numbers, first n even numbers, and first n odd numbers — all derivable from the Sₙ formula. Exercise 5.3 is the most important exercise in this chapter and is filled with word problems involving money saved over days, logs stacked in rows, seats arranged in a theatre, and similar real-life APs.
| Question Type | Typical Marks | Frequency in Board Exams |
| Find nth term of an AP | 1–2 Marks | Very High |
| Find number of terms in an AP | 2 Marks | High |
| Sum of first n terms | 3 Marks | Very High |
| Word problem using AP sum | 4 Marks | High |
| Find a and d given two conditions | 3–4 Marks | High |
| Check if list of numbers is AP | 1 Mark | Medium (MCQ) |
NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions
An arithmetic progression, commonly called an AP, is a sequence of numbers in which the difference between consecutive terms remains constant. This constant difference is known as the common difference. Examples include sequences such as 2, 5, 8, 11 and 10, 20, 30, 40. Arithmetic progressions help students understand patterns and relationships between numbers. This chapter focuses on finding terms, sums, and properties of APs. Understanding arithmetic progressions is important because they are widely used in mathematics, finance, and everyday situations involving regular increases or decreases.
The nth term of an arithmetic progression is found using a formula that involves the first term, common difference, and the position of the term. This formula allows students to determine any term directly without listing all previous terms. It is especially useful when finding large-position terms such as the hundredth or thousandth term. Understanding the nth term concept helps students identify patterns and solve sequence-based problems efficiently. Examination questions often focus on finding missing terms and determining positions within an arithmetic progression.
The common difference is the fixed value added to or subtracted from each term to obtain the next term in the sequence. It is found by subtracting any term from the term immediately following it. The common difference determines whether the sequence is increasing, decreasing, or constant. A positive common difference produces an increasing sequence, while a negative one creates a decreasing sequence. Understanding this concept is essential because most calculations in arithmetic progression depend on correctly identifying the common difference.
The sum of n terms of an arithmetic progression can be calculated using a specific formula involving the first term, number of terms, and common difference. This method eliminates the need to add every term individually, making calculations much faster. Students learn how to apply the formula to solve practical problems involving consecutive numbers and regular patterns. Questions on finding sums are frequently asked in examinations because they test understanding of both formulas and sequence properties. Mastering this concept improves problem-solving efficiency.
Arithmetic progressions appear in many real-life situations. Examples include monthly savings plans, regular salary increments, seating arrangements, and patterns in construction designs. Whenever quantities increase or decrease by a fixed amount, arithmetic progression concepts can be applied. Learning these applications helps students appreciate the practical usefulness of mathematics. Real-life examples also make the chapter easier to understand because students can connect theoretical concepts with everyday experiences. Such applications highlight the importance of arithmetic progressions beyond academic studies.
To determine whether a sequence is an arithmetic progression, calculate the difference between consecutive terms. If the difference remains constant throughout the sequence, it is an AP. If the difference changes, the sequence is not an arithmetic progression. This simple method helps students classify sequences quickly and accurately. Understanding how to identify APs is important because many examination questions begin with determining whether a given sequence satisfies the conditions of an arithmetic progression before performing further calculations.
Many students incorrectly calculate the common difference or use the wrong value for the first term. Errors also occur while substituting values into formulas or interpreting word problems. Some students confuse the nth term formula with the sum formula, leading to incorrect answers. To avoid mistakes, it is important to identify the given information carefully and select the correct formula. Regular practice helps improve accuracy and confidence. Developing a systematic approach ensures better performance in arithmetic progression questions during examinations.