Chapter 8 · Class XI Mathematics · NCERT Exercises

Sequences & Series — Exercises

AP · GP · HP · AGP — Every Sequence & Series Exercise Fully Solved

📂 3 Exercises 📝 64 Questions 🎓 High

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 8.1

AP — nth term · sum · properties

14 Q Easy

②

Exercise 8.2

GP — nth term · sum · infinite GP

32 Q Moderate

★

Miscellaneous

AGP · telescoping · HP · combined series

18 Q Hard

3 exercise files · 64 total questions

Chapter at a Glance

JEE MainJEE AdvancedCBSE BoardsBITSATKVPY

13Concepts

25Formulas

HighDifficulty

8–10%Weightage

Before You Begin

Prerequisites

✓Basic algebra — simultaneous equations
✓Exponent rules
✓Ch 7 Binomial (for some series)

Have Ready

🔧Formula card: AP/GP/HP
🔧Σn, Σn², Σn³ standard results

Exercise Topic Map

Exercise 8.1aₙ=a+(n−1)d; Sₙ=n/2[2a+(n−1)d]; insert arithmetic means

Exercise 8.2aₙ=arⁿ⁻¹; Sₙ; infinite GP S∞=a/(1−r); geometric means

MiscellaneousSum of AGP; HP to AP conversion; telescoping; recurring decimals

Key Formulae

\(a_n = a+(n-1)d;\quad S_n = \tfrac{n}{2}[2a+(n-1)d]\)

\(S_\infty = \dfrac{a}{1-r},\quad |r|<1\)

\(AM \geq GM \geq HM;\text{ equality when }a=b\)

\(\sum k = \tfrac{n(n+1)}{2};\quad \sum k^2 = \tfrac{n(n+1)(2n+1)}{6};\quad \sum k^3 = \!\left[\tfrac{n(n+1)}{2}\right]^2\)

NCERT Solving Method

Step 1 — Identify type in 5 seconds: constant difference→AP; constant ratio→GP; reciprocals form AP→HP. Step 2 — Write a,d (or r) before applying any formula. Step 3 — AM-GM: group terms so product is constant, then apply AM≥GM. Step 4 — HP: take reciprocals, solve as AP, reciprocate the answer.

Continue Your Preparation

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