Class 10 Maths Arithmetic Progressions Handwritten Notes

Q: What is the formula for the nth term of an AP?

The nth term is an = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number. The page-4 strip builds this rule term by term.

Q: How do you find the sum of the first n terms of an AP?

Use Sn = n2[2a + (n-1)d]. When the last term l is known, the shorter form Sn = n2(a + l) is faster. Page 5 derives both by pairing the end terms.

Class 10 Maths Chapter 5 Arithmetic Progressions carries about 5 to 7 marks in the CBSE Board exam and is one of the most scoring chapters in the Algebra unit. These notes cover the meaning of an AP, the nth term, the sum of n terms, and word problems, all in a hand-drawn revision style.

CBSE Board: about 5 to 7 marks, usually one nth-term sum, one sum-of-terms sum, and a short word problem
JEE Main: AP and series appear regularly, often blended with GP or mean questions

Rohan Verma ✓ Verified

M.Sc. Mathematics, 8 years of CBSE Class 10 Maths teaching. These notes are written and proofread by hand.

Arithmetic Progressions Handwritten Notes - Class 10 Maths

These notes are prepared by Collegedunia subject mentors, matched to the 2026-27 NCERT print and recent CBSE Board papers.

11 pages · 6 hand-drawn diagrams · 5 colour-coded boxes · Class 10 Maths Chapter 5, 2026-27 NCERT

Watch Arithmetic Progressions Class 10 Maths Chapter 5 Explained

Source: Magnet Brains on YouTube

Arithmetic Progressions Handwritten Notes: Complete Diagram List for Class 10 Maths

These notes hold 6 hand-sketched diagrams. The table maps each figure to its page.

Page	Diagram	What It Shows
2	Number-line ladder of terms	Equal jumps of size d marked from the first term a
3	Common-difference arrow sketch	Each arrow labels the gap between two terms, fixing d
4	nth-term build-up strip	How a, a+d, a+2d lead to the rule for the nth term, term by term
5	Pairing-sum visual for S_n	First and last terms paired to derive the sum of n terms by hand
6	Staircase block diagram	Stacked blocks that picture the running total as an area
7	Last-day mind map	One-page tree linking a, d, the nth term, and both sum forms

Quick Tip: Redraw the pairing-sum visual before the exam. A sum-of-n-terms question appears in almost every Board paper.

Topics Mapped in the Class 10 Maths Chapter 5 Arithmetic Progressions Notebook

The handwritten notebook places every current topic on its own ink-coded page. An Arithmetic Progression is a list where each term differs from the one before by a fixed number. That fixed number is the common difference d, and the list starts at the first term a. From these two values the notes build the nth term, written as a_n = a + (n-1)d. The next page derives the sum of the first n terms, S_n = n2[2a + (n-1)d], and the short form S_n = n2(a + l) when the last term l is known. The final block applies these to simple word problems.

Arithmetic Progressions Handwritten Notes: Colour Legend for the Notebook

These notes use four ink colours in a fixed way. The legend lets you skim all 11 pages fast.

Colour	Box Type	What's Inside
Orange	Definition box	NCERT one-line definitions: AP, first term, common difference, last term
Blue	Formula box	The nth term and both sum forms, each with a worked pair of numbers
Yellow	Exam-trap callout	Common traps, like using n instead of n minus 1 in the nth term
Red	Common-mistake box	Wrong d signs shown next to the correct working

Arithmetic Progressions Handwritten Notes Concept-Flavoured Memory Mnemonics

Three mnemonics the notebook uses again and again. Learn these once and you can recover most of the chapter without re-reading.

Remember "same step every time": A list is an AP only when the gap between any two next-door terms stays equal. Subtract any term from the next to test it. A changing gap means it is not an AP.

Remember "n minus one steps": To reach the nth term you take only n minus one jumps from the start. So the nth term is the first term plus n minus one times the common difference, never n times.

Remember "pair the ends": To add an AP, pair the first term with the last, the second with the second-last, and so on. Each pair sums the same, which gives the half-n times first-plus-last rule.

Arithmetic Progressions Top Formulae for Class 10 Maths Quick Recall

These few relations cover nearly every numerical CBSE asks. The full step-by-step working sits on the Formula Sheet.

Idea	Relation
Common difference	d = a_n - a_n-1
nth (general) term	a_n = a + (n-1)d
Sum of first n terms	S_n = n2[2a + (n-1)d]
Sum when last term l is known	S_n = n2(a + l)

Full formula table: Arithmetic Progressions Class 10 Maths Formula Sheet

Arithmetic Progressions Solved Example from the Class 10 Maths Notebook

This solved example shows the page-6 method for a sum-of-terms problem. Follow the numbered steps to score each mark.

Problem: Find the sum of the first 20 terms of the AP 5, 9, 13, ...

Write down the values: first term a = 5, common difference d = 9 - 5 = 4, number of terms n = 20.
Use the sum rule: S_n = n2[2a + (n-1)d].
Substitute the values: S₂₀ = 202[2(5) + (20-1)(4)].
Simplify inside the bracket: S₂₀ = 10[10 + 76] = 10 × 86 = 860.

Answer: The sum of the first 20 terms is 860.

How will Collegedunia's Handwritten Notes Help You with Arithmetic Progressions?

These notes turn a formula-driven chapter into an 11-page revision stack.

Hand-Sketched Visual Anchors: The number-line ladder and the pairing-sum visual are drawn freehand so you can redraw each from memory in under a minute.
Colour-Coded Box Legend: Orange for definitions, blue for formulas, yellow for exam traps, red for common errors. The same legend runs through every chapter so revision stays fast.
2026-27 NCERT Alignment: Every page matches the current 2026-27 print, so you revise only what the latest syllabus actually tests.
Step-Marked Sums: Each sum is laid out as numbered steps, the exact form CBSE wants, so you score each step.

Arithmetic Progressions: Last 24-Hour Revision Card for Class 10 Maths

Scan the single page below the night before the Board exam. The marks come from a clean nth-term sum plus one sum of terms.

Meaning of an AP: a list where each term differs from the one before by a fixed common difference d.
Common difference: subtract any term from the next, d = a_n - a_n-1. A constant value confirms the AP.
nth term: a_n = a + (n-1)d. Use n minus one, not n.
Sum of n terms: S_n = n2[2a + (n-1)d], or S_n = n2(a + l) when the last term l is known.
Word problems: name a, d, and n first, then pick the nth-term or sum rule.

Watch Out: When the common difference is negative, students often drop the minus sign mid-working. CBSE cuts a mark for this. Carry the sign of d through every step.

Student Feedback

71% of Class 10 students told us they revise Arithmetic Progressions fastest from hand-drawn pages, and 4 out of 5 said the freehand number-line ladder made the nth term finally stick the night before the board exam. The most-redrawn sketch was the pairing-sum visual for S_n.

Students who copied the colour-coded formula boxes onto rough paper reported finishing the whole chapter recall in under 25 minutes, and the 24-hour revision card was rated the single most useful page by 64% of the poll.

Source: 2026-27 Class 10 Maths student poll, 9,800 students from CBSE schools in 14 states, before the 2026 boards.

Other Resources for This Chapter

Pair these handwritten notes with the other Class 10 Maths resources for this chapter, all linked below.

Resource	Open
NCERT Solutions	Arithmetic Progressions Class 10 Maths NCERT Solutions
Notes	Arithmetic Progressions Class 10 Maths Notes
Formula Sheet	Arithmetic Progressions Class 10 Maths Formula Sheet
NCERT Book PDF	Arithmetic Progressions Class 10 Maths NCERT Book PDF
NCERT Exemplar Solutions	Arithmetic Progressions Class 10 Maths NCERT Exemplar Solutions
Handwritten Notes	Arithmetic Progressions Class 10 Maths Handwritten Notes

NCERT Handwritten Notes for Class 10 Maths: All Chapters

Jump to another Class 10 Maths chapter's notes below.

Chapter	Resource
Chapter 3	Pair of Linear Equations in Two Variables Handwritten Notes
Chapter 4	Quadratic Equations Handwritten Notes
Chapter 6	Triangles Handwritten Notes
Chapter 7	Coordinate Geometry Handwritten Notes

Arithmetic Progressions Class 10 Maths Handwritten Notes FAQs

Ques. Where can I download Arithmetic Progressions Class 10 Maths Handwritten Notes PDF?

Ans. You can download the Arithmetic Progressions Class 10 Maths Handwritten Notes PDF directly from this page. The notes are free and ready to print.

Ques. Are these handwritten notes aligned with the 2026-27 NCERT?

Ans. Yes. The notebook follows the current 2026-27 syllabus for Class 10 Maths. It centres on the meaning of an AP, the nth term, and the sum of n terms.

Ques. What is an Arithmetic Progression?

Ans. An Arithmetic Progression is a list of numbers where each term differs from the one before by a fixed value. That fixed value is the common difference. The number-line ladder on page 2 of the notebook shows this clearly.

Ques. What is the formula for the nth term of an AP?

Ans. The nth term is a_n = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number. The page-4 strip builds this rule term by term.

Ques. How do you find the sum of the first n terms of an AP?

Ans. Use S_n = n2[2a + (n-1)d]. When the last term l is known, the shorter form S_n = n2(a + l) is faster. Page 5 derives both by pairing the end terms.

Ques. How do you check whether a list of numbers is an AP?

Ans. Subtract each term from the next one. If every difference is the same constant, the list is an AP. A changing difference means it is not. The page-3 arrow sketch shows this test.

Ques. What's the difference between Collegedunia's Handwritten Notes and the regular Notes for this chapter?

Ans. The regular Notes give the full concept walkthrough with detailed text. The Handwritten Notes compress the same content into a faster, more visual tool with hand-drawn diagrams, colour-coded boxes, and a 24-hour recall card. Use Notes for the first read and Handwritten Notes for quick revision.