aₙ = a + (n−1)d Sₙ = n/2·[2a+(n−1)d] +d +d
a,a+d,…
Chapter 5  ·  Class X Mathematics

The Beauty of Linear Sequences

Arithmetic Progressions

Every Pattern Has a Formula — Find the Term, Find the Sum

📖 Read Full Notes ⚡ Formula Capsules

Chapter Snapshot

7Concepts
5Formulae
8–10%Exam Weight
4–5Avg Q's
Easy-ModerateDifficulty

Why This Chapter Matters for Exams

CBSE BoardNTSEState BoardsOlympiad

AP is one of the most scoring chapters in Class X Boards with 8–10 marks available. "Find the nth term" and "find the sum" are guaranteed question types. The chapter is almost entirely formula-driven, making it high ROI. NTSE has elegant AP-based sequence reasoning problems.

Key Concept Highlights

Definition of AP
Common Difference
General Term (nth Term)
Sum of First n Terms
Arithmetic Mean
Finding Terms Given Conditions
AP in Real-Life Contexts
Problems on Sum and Terms

Important Formula Capsules

$a_n = a + (n-1)d$
$S_n = \dfrac{n}{2}[2a + (n-1)d]$
$S_n = \dfrac{n}{2}[a + l]\ (l = \text{last term})$
$\text{AM of a and b} = \tfrac{a+b}{2}$
$d = a_2 - a_1\ (\text{common difference})$

What You Will Learn

Navigate to Chapter Resources

📖 Full Notes Complete NCERT Coverage 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT Solutions ✔️❌ True / False Concept-based True & False

🏆 Exam Strategy & Preparation Tips

This is a guaranteed marks chapter — target 100% accuracy. Practise problems where both the term formula and sum formula are needed simultaneously. "Middle term of AP" and "AP with given sum" are common twists. Time investment: 2 days.


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