R
Rishtaara
Mathematics · Class 11

Sequences and Series

Learn Sequences and Series with notes, examples, and practice questions.

3 sections15–25 min read6 MCQs · 2 examples

Chapter Overview

Sequences are ordered lists; series are sums of sequence terms. AP, GP, and special sums like Σn and Σn² appear throughout board papers.

AP & GP

AP nth term

aₙ = a + (n−1)d

AP sum

Sₙ = n/2 [2a + (n−1)d]

GP nth term

aₙ = arⁿ⁻¹

GP sum (r≠1)

Sₙ = a(1−rⁿ)/(1−r)

Infinite GP

S∞ = a/(1−r), |r|<1

Special Sums

Σk

n(n+1)/2

Σk²

n(n+1)(2n+1)/6

Σk³

[n(n+1)/2]²

Solved Examples

Step-by-step solutions — read each step before checking the final answer.

AP sum

Sum of first 20 terms: a=3, d=2.

  1. 1S₂₀=20/2[6+38]=440

Answer

440

GP infinite

a=4, r=1/2.

  1. 1S∞=4/(1−1/2)=8

Answer

8

Key Points to Remember

  • AM between a,b: (a+b)/2
  • GM: √(ab)
  • Relationship AM ≥ GM

Exam Tips

  • Identify AP or GP from problem
  • Check |r|<1 for infinite GP

Practice MCQs — Sequences and Series

Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.

Question 1 of 6Score: 0/0

AP common difference is: