Revision Notes: Class 10 Maths Chapter 5 Arithmetic Progressions

A fast, one-glance recap of Class 10 Maths Chapter 5 (Arithmetic Progressions) — for full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 5 notes are ideal for quick revision just before exams.

Last Updated: October 24, 2026

Common Mistakes Students Make in Arithmetic Progressions

Why This Chapter Matters

Arithmetic Progressions is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

Revision Notes: Arithmetic Progressions

• AP definition: a sequence where the difference between any two consecutive terms is constant (the common difference, d)
• General form: a, a+d, a+2d, a+3d, …
• nth term: aₙ = a + (n−1)d
• nth term from the end (when last term l is known): treat l as first term with common difference −d
• Sum of first n terms (when a, d known): Sₙ = (n/2)[2a + (n−1)d]
• Sum of first n terms (when a, last term l known): Sₙ = (n/2)(a + l)
• nth term from sums: aₙ = Sₙ − Sₙ−₁
• Three consecutive AP terms are often taken as (a−d), a, (a+d) for easier algebra (sum = 3a)
• Removed from current syllabus: Exercise 5.4 (optional exercise) is not part of the 2026-27 rationalised syllabus
• Common exam traps: confusing “nth term” with “sum of n terms”; forgetting the (n−1) in aₙ; sign errors when d is negative

Related: Solutions | Extra Questions | Revision Notes | Formulas Handbook | Class 10 Maths Book

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Frequently Asked Questions

What is the formula for the nth term of an arithmetic progression?
a_n = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number — this single formula is the starting point for the vast majority of AP problems.

What is the formula for the sum of the first n terms of an AP?
S_n = n/2 [2a + (n-1)d], or equivalently S_n = n/2 (a + a_n) when the last term is known — both forms are used interchangeably depending on what information a question provides.

What to Revise First (and Last) in This Chapter

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.