Chapter 16 of 27
Revision Notes
Sequences And Series — Revision Notes
KEAM · Mathematics
Quick revision notes for Sequences And Series — key concepts, formulas, and definitions for KEAM Mathematics preparation.
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Key concepts, formulas, and definitions from Sequences And Series for KEAM Mathematics preparation.
Key Topics to Revise
1
Basic Concepts - Sequences and Series
- A sequence is a function from natural numbers to real numbers, denoted as {a₁, a₂, a₃, ...}
- A series is the sum of terms of a sequence: a₁ + a₂ + a₃ + ...
- Finite sequences have limited terms, infinite sequences continue indefinitely
2
Arithmetic Progression (A.P.)
- Each term is obtained by adding a fixed number (common difference) to the previous term
- General form: a, a+d, a+2d, a+3d, ... where 'a' is first term, 'd' is common difference
- Can have positive, negative, or zero common difference
3
Geometric Progression (G.P.)
- Each term is obtained by multiplying the previous term by a fixed non-zero number (common ratio)
- General form: a, ar, ar², ar³, ... where 'a' is first term, 'r' is common ratio
- Common ratio can be positive, negative, or fraction (but not zero)
4
Relationship Between A.M. and G.M.
- For two positive numbers a and b: A.M. ≥ G.M.
- Equality holds when a = b
- A.M. - G.M. = (√a - √b)²/2 ≥ 0
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Key Concepts
A sequence is a function fSequence where each term equals previousSequence where each term equals previousASum of first n natural numbers
Frequently Asked Questions
What topics are covered in Sequences And Series for KEAM?
Sequences And Series is an important chapter in KEAM Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts - Sequences and Series, Arithmetic Progression (A.P.), Geometric Progression (G.P.), Relationship Between A.M. and G.M..
How important is Sequences And Series for KEAM?
Sequences And Series is a frequently tested chapter in KEAM Mathematics. Questions from this chapter appear regularly in previous year papers. There are 283 practice questions available for this chapter.
How to prepare Sequences And Series for KEAM?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
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