Sequences and Series – Class 11 Maths (NCERT Based)
The chapter Sequences and Series is a fundamental part of Class 11 Mathematics. It deals with patterns of numbers and provides formulas to handle large sets of numbers efficiently. This chapter is widely used in algebra, calculus, and competitive exams.
This content is strictly NCERT-aligned and written in simple, student-friendly language.
📖 What is a Sequence?
A sequence is an ordered list of numbers. Each number is called a term.
- Example: 2, 4, 6, 8, … (Arithmetic sequence)
- Example: 1, 2, 4, 8, … (Geometric sequence)
🔹 Types of Sequences
1. Arithmetic Progression (AP)
A sequence in which the difference between consecutive terms is constant.
- nth term (Tn): Tn = a + (n − 1)d
- Sum of first n terms (Sn): Sn = n/2 × [2a + (n − 1)d]
- Where:
- a = first term
- d = common difference
Example: 3, 7, 11, 15, …
- a = 3, d = 4
- T5 = 3 + (5 − 1)×4 = 19
2. Geometric Progression (GP)
A sequence in which the ratio between consecutive terms is constant.
- nth term (Tn): Tn = ar^(n − 1)
- Sum of first n terms (Sn): Sn = a(1 − r^n)/(1 − r), r ≠ 1
- Sum to infinity (S∞): S∞ = a/(1 − r), |r| < 1
- Where:
- a = first term
- r = common ratio
Example: 2, 4, 8, 16, …
- a = 2, r = 2
- T4 = 2 × 2^(4 − 1) = 16
🔹 Important Formulas
| Formula | Description |
|---|---|
| Tn = a + (n − 1)d | nth term of AP |
| Sn = n/2 [2a + (n − 1)d] | Sum of first n terms of AP |
| Tn = ar^(n − 1) | nth term of GP |
| Sn = a(1 − r^n)/(1 − r) | Sum of first n terms of GP |
| S∞ = a/(1 − r) | Sum to infinity of GP, |