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.
- 1S₂₀=20/2[6+38]=440
Answer
440
GP infinite
a=4, r=1/2.
- 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: