NCERT Class 10 Mathematics Mathematics: Chapter 5 — 1 Introduction
This chapter introduces the concept of Arithmetic Progressions (APs) in Mathematics for Class 10 CBSE students. It begins by highlighting patterns observed in nature and daily life, such as salary increments, ladder rung lengths, savings schemes, and number sequences. The chapter defines an AP as a sequence where the difference between consecutive terms is constant, known as the common difference. It provides examples like salary progression and savings amounts to illustrate this concept. The text aims to help students understand and identify arithmetic progressions, laying the foundation for further exploration of their properties and applications in problem-solving within the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 5 — 1 Introduction |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 402 |
Learning outcomes
- Understand the concept of patterns in sequences.
- Define an Arithmetic Progression (AP).
- Identify the common difference in an AP.
- Recognize real-world examples of APs.
Vocabulary
| Word | Meaning |
|---|---|
| Pattern | A regular and intelligible form or sequence. |
| Sequence | A set of numbers or events in a particular order. |
| Arithmetic Progression | A sequence of numbers such that the difference between the consecutive terms is constant. |
| Common Difference | The constant difference between consecutive terms in an arithmetic progression. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- Identify a pattern in the sequence of salaries: 8000, 8500, 9000,... Answer: The pattern is an annual increment of 500.
- What is the common difference in the sequence of ladder rung lengths: 45, 43, 41,...? Answer: The common difference is -2 cm.
- Is the sequence 1, 1, 2, 3, 5, 8 an Arithmetic Progression? Explain. Answer: No, because the difference between consecutive terms is not constant (1-1=0, 2-1=1, 3-2=1, 5-3=2).
Frequently asked questions
What is an Arithmetic Progression (AP)?
An Arithmetic Progression is a sequence of numbers where the difference between any two successive members is constant.
What is the common difference in an AP?
The common difference is the constant value obtained by subtracting any term from its succeeding term in an AP.
Can you give an example of an AP from daily life?
Yes, a salary with a fixed annual increment, like 8000, 8500, 9000,... is an AP.
What is the first term in the ladder rung example?
The first term (bottom rung) is 45 cm.
What kind of patterns are discussed in the introduction?
Patterns in nature (sunflower petals, honeycomb) and daily life (salaries, savings, measurements).
Related resources
Important topics
Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 5 — 1 Introduction. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.