Chapter 5 · Class X Mathematics · NCERT Exercises

Arithmetic Progressions — Exercises

nth Term · Sum · Applications — All 35 AP Problems Solved

📂 4 Exercises 📝 51 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

Identify AP; find first term, common difference

nth term formula; find specific terms; find n given aₙ

Sum of n terms Sₙ; find n given Sₙ; application problems

20 Q Moderate-Hard

Mixed — combined AP conditions; real-world series; two-AP comparisons

4 exercise files · 51 total questions

Chapter at a Glance

CBSE BoardsNTSEJEE Foundation

7 Concepts

6 Formulas

Moderate Difficulty

8–10% Weightage

Before You Begin

Prerequisites

✓Number patterns (Class VIII)
✓Algebraic manipulation
✓Basic equation solving

Have Ready

🔧AP formula card
🔧Graph paper for visual series

Exercise Topic Map

Exercise 5.1 Check constant difference: a₂−a₁ = a₃−a₂; list first few terms

Exercise 5.2 aₙ = a+(n−1)d; solve for unknown (a,d, or n) algebraically

Exercise 5.3 Sₙ = n/2[2a+(n−1)d] or Sₙ = n/2[a+l]; set up equations with two conditions

Miscellaneous Frame simultaneous equations from two AP conditions; solve as a system

Key Formulae — Recall Before Solving

\(a_n = a + (n-1)d\)

\(S_n = \dfrac{n}{2}[2a + (n-1)d] = \dfrac{n}{2}(a + l)\)

\(d = a_2 - a_1 = a_3 - a_2 = \cdots\)

\(a_n = S_n - S_{n-1} \quad (n \ge 2)\)

NCERT Solving Method

Step 1 — Always extract a and d before applying any formula. Step 2 — Two unknowns: set up two equations from two given conditions; solve simultaneously. Step 3 — For Sₙ problems with quadratic form (Sₙ = pn²+qn): nth term = Sₙ − Sₙ₋₁. Step 4 — Word problems: identify what forms the AP (years, rows, bounces etc.); define a and d clearly.

Continue Your Preparation

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