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: July 21, 2026

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.

Written by Satish

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