TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27

Chapter 5: Arithmetic Progressions

Detailed Notes • Worked Examples • Competency • Board Practice

📖 Chapter Explanation

An arithmetic progression is a sequence in which the difference between consecutive terms remains constant. The chapter develops the nth-term and sum formulas and uses them to model regular growth in real situations.

🧭 Concept Journey

sequence → common difference → nth term → sum of n terms → modelling

📌 Core Concepts

For an AP with first term a and common difference d, aₙ=a+(n−1)d and Sₙ=n/2[2a+(n−1)d]. For 7,11,15,…, a=7 and d=4, so a₁₀=43.

💡 Worked Example

The nth-term formula describes one position; the sum formula describes the total of the first n positions. Choosing the correct formula is part of solving the problem.

🔍 Understanding the Idea

For an AP with first term a and common difference d, aₙ=a+(n−1)d and Sₙ=n/2[2a+(n−1)d]. For 7,11,15,…, a=7 and d=4, so a₁₀=43.

⚠️ Common Errors

Do not confuse the nth term with the sum of n terms. Also check whether the common difference is positive or negative.

🧠 Concept-Based MCQs

The common difference of 5,9,13,17 is: A) 3 B) 4 C) 5 D) 9
The 10th term of 3,7,11,… is: A) 35 B) 39 C) 43 D) 47
The sum formula for an AP uses: A) only d B) only n C) a,d,n D) only the last term
If d=0, the AP is: A) constant B) decreasing only C) geometric D) undefined

Answer Key: 1-B, 2-B, 3-C, 4-A.

📊 Case-Based / Competency

A stadium has 20 seats in the first row and each successive row has 4 more seats. Find the number of seats in the 15th row and the total seats in the first 15 rows.

Identify the variables or mathematical structure.
Form the required mathematical representation.
Solve systematically.
Interpret and verify the result.

🔎 Extension Case

A theatre adds the same number of seats to every new row. Students model the row capacities as an AP, calculate a specified row and total capacity, then explain why the model is appropriate.

🔥 HOTS & Board Challenge

Explain why the chosen method works.
Create a similar problem with different values and solve it.
Find and correct a plausible incorrect solution.
Connect the concept to a real-life situation.

✍️ Exam Practice

Define the central concept with an example.
Solve a direct application problem with complete steps.
Solve a multi-step competency problem.
Interpret a graph/table/context where applicable.
Write a 5-mark answer with reasoning and verification.

📄 Practice Worksheet

5 concept checks
5 standard problems
3 application problems
2 case-based problems
2 HOTS problems
1 board-style challenge

🎯 One-Minute Revision