📐 CBSE · Class 10 · Mathematics · Chapter 5

Arithmetic
Progressions

Complete chapter resources for CBSE Class 10 Maths — topic breakdown, key AP formulas, sample questions, previous year board questions, and instant AI question paper generation.

4Topics
5–8Board marks
8Sample questions
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Key Formulas — Chapter 5
  • General term: aₙ = a + (n−1)d
  • Sum of n terms: Sₙ = n/2 × [2a + (n−1)d]
  • Sum (last term known): Sₙ = n/2 × (a + l)
  • Common difference: d = aₙ − aₙ₋₁
  • nth term from end: aₙ = l − (n−1)d
  • Middle term (odd n): a₍ₙ₊₁₎/₂ = Sₙ / n
Chapter Overview

What this chapter covers

An Arithmetic Progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference (d), to the preceding term. The sequence is completely determined by its first term a and its common difference d. Identifying whether a given list of numbers forms an AP — and finding d — is the foundation of this chapter.

The two core formulas are the nth term formula (aₙ = a + (n−1)d) and the sum of n terms formula (Sₙ = n/2 × [2a + (n−1)d]). Together these allow students to find any term in the sequence, determine how many terms the sequence has, locate the middle term, and calculate partial sums. A useful alternate form, Sₙ = n/2 × (a + l), applies when the last term l is known directly.

Board questions in this chapter consistently include word problems where a real-world situation — rows of seats in an auditorium, monthly savings, stacked logs — must first be modelled as an AP and then solved using the nth term or sum formula. These 4–5 mark problems require students to correctly identify a and d from the problem context before applying any formula.

Topics

What's inside Chapter 5

As per NCERT Class 10 Mathematics (CBSE syllabus)

Topic 1
Introduction to Arithmetic Progressions
Definition of a sequence, finite vs. infinite AP, identifying an AP by checking for a constant common difference between consecutive terms. Examples from real life — daily savings, equal jumps on a number line.
Topic 2
nth Term of an AP
Deriving and applying the formula aₙ = a + (n−1)d. Finding a specific term, determining n when aₙ is given, and checking whether a given value is a term of the AP.
Topic 3
Sum of First n Terms
Deriving Sₙ = n/2 × [2a + (n−1)d] and the alternate form Sₙ = n/2 × (a + l). Using the sum formula to find n when Sₙ is given, and relating aₙ = Sₙ − Sₙ₋₁.
Topic 4
Applications of AP
Word problems involving rows of objects, financial planning (fixed deposits, savings schemes), distance-time with uniform acceleration, and problems where terms of an AP satisfy given conditions.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Ch 4 · Quadratic Equations
Sum-of-n-terms problems sometimes yield quadratic equations in n
Ch 1 · Real Numbers
Number patterns, divisibility, and arithmetic on integers
Chapter 5 Arithmetic
Progressions
Leads to
Class 11 · Sequences & Series
Geometric progressions, harmonic progressions, infinite series
Class 11 · Binomial Theorem
Summation notation and pattern recognition in expansions
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 10 board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1–2 Identify AP, find common difference, or find a specific term
Very Short Answer 2 1 Find nth term or check if a value belongs to the AP
Short Answer 3 1 Sum of n terms or finding n when sum is given
Long Answer / Word Problem 4–5 1 Real-life application — seating, savings, stacked objects
Total (approximate) 5–8 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 10 Maths Chapter 5. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The common difference of the AP: 3, 1, −1, −3, … is: (a) 2 (b) −2 (c) 1 (d) −1
Q2 Easy 2 marks Short Answer
Find the 20th term of the AP: 7, 13, 19, 25, …
Q3 Medium 2 marks Short Answer
The 5th term of an AP is 26 and its 10th term is 51. Find the first term and the common difference.
Q4 Medium 3 marks Short Answer
Find the sum of the first 25 terms of the AP: 2, 7, 12, 17, …
Q5 Medium 3 marks Short Answer
How many terms of the AP: 9, 17, 25, … must be taken so that their sum equals 636?
Q6 Hard 4 marks Word Problem
The sum of three consecutive terms of an AP is 27 and their product is 504. Find the three terms.
Q7 Hard 4 marks Word Problem
A contract on construction work stipulates a penalty for delay. The penalty for the first day is ₹200, for the second day ₹250, for the third day ₹300, and so on — increasing by ₹50 each day. How much penalty does the contractor pay if he delays the work by 30 days?
Q8 Hard 5 marks Case-Based
An auditorium has seats arranged so that the first row has 20 seats, the second row has 22 seats, the third row has 24 seats, and so on. (i) How many seats are in the 15th row? (ii) If there are 30 rows in all, what is the total seating capacity? (iii) In which row are there 50 seats?
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 10 Maths board papers — Arithmetic Progressions chapter.

Board 20222 marks
Find the number of terms in the AP: 18, 15½, 13, …, −47. (CBSE Delhi 2022)
Board 20233 marks
The first term of an AP is 5, the last term is 45, and the sum of all its terms is 400. Find the number of terms and the common difference. (All India 2023)
Board 20204 marks
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees that each section of each class will plant will be the same as the class number in which they are studying — Class 1 plants 1 tree, Class 2 plants 2 trees, …, Class 12 plants 12 trees. There are 3 sections of each class. How many trees will be planted by all the students of the school? (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Arithmetic Progressions carry in the CBSE Class 10 board exam? +
Typically 5–8 marks across 3–4 questions — one 1-mark MCQ on identifying an AP or the common difference, one 2-mark question on the nth term, and one 4–5 mark word problem involving the sum of n terms. The chapter has appeared in every CBSE Class 10 Maths board paper in recent years and is considered a high-scoring chapter with predictable question patterns.
What is the difference between the nth term formula and the sum formula in AP? +
The nth term formula aₙ = a + (n−1)d gives the value of a specific term in the sequence. The sum formula Sₙ = n/2 × [2a + (n−1)d] (or equivalently Sₙ = n/2 × (a + l) when the last term l is known) gives the total of the first n terms. Board questions often use both together — for example, finding how many terms sum to a given value requires setting Sₙ equal to that value and solving for n.
How do I identify whether a sequence is an AP in board exams? +
A sequence is an AP if the difference between every pair of consecutive terms is constant. Check: a₂ − a₁ = a₃ − a₂ = d (the common difference). If this holds, the sequence is an AP. Board MCQs and 1-mark questions frequently ask students to find d or identify the AP from a list of sequences — verify the constant difference for all adjacent pairs, not just the first two.
What are the most common word-problem themes from this chapter in board exams? +
The four recurring themes are: (1) savings/deposits growing by a fixed amount each month, (2) rows of seats or objects arranged in an AP pattern, (3) distance-time problems where speed increases by a fixed amount, and (4) finding the number of terms when the sum or a specific term equals a given value. These 4–5 mark problems almost always require students to set up the AP, identify a and d, and then apply either the nth term or sum formula.
How do I generate a custom question paper for Arithmetic Progressions using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 10 Mathematics, select Chapter 5 (Arithmetic Progressions), set your preferred question-type mix (MCQ, short answer, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.