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Sequence and Series
Sequence and Series
Sequence and Series – JEE Mains Mathematics
by Zenith LMS
Updated April 2025
1. Arithmetic Progression (A.P.)
A sequence where the difference between consecutive terms is constant.
General form: a, a+d, a+2d, ..., a+(n−1)d
n-th term: T
n
= a + (n−1)d
Sum of first n terms: S
n
= (n/2)[2a + (n−1)d] or S
n
= (n/2)(a + l)
2. Geometric Progression (G.P.)
A sequence where each term is obtained by multiplying the previous term by a constant ratio.
General form: a, ar, ar², ar³, ..., ar
n−1
n-th term: T
n
= ar
n−1
Sum of first n terms (r ≠ 1): S
n
= a(1 − rⁿ)/(1 − r)
Sum to infinity (|r| < 1): S = a/(1 − r)
3. Insertion of A.M. and G.M. Between Two Numbers
To insert n arithmetic means between a and b:
Use A.P. formula with a as the first term and b as the (n+2)
th
term.
d = (b − a)/(n+1), then insert values using a + d, a + 2d, ...
To insert n geometric means between a and b:
Use G.P. with a as the first term and b as the (n+2)
th
term: b = ar
n+1
r = (b/a)
1/(n+1)
4. Relation Between A.M. and G.M.
For any two positive numbers a and b:
A.M. = (a + b)/2
G.M. = √(ab)
Relation: A.M. ≥ G.M., with equality only when a = b
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JEE Mains Physics
Units and Measurements
Kinematics
Laws of Motion
Work, Energy and Power
Rotational Motion
Gravitation
Properties of Solids and Liquids
Thermodynamics
Kinetic Theory of Gases
Oscillations and Waves
Electrostatics
Current Electricity
Magnetic Effects of Current and Magnetism
Electromagnetic Induction and Alternating Currents
Electromagnetic Waves
Optics
Dual Nature of Matter and Radiation
Atoms and Nuclei
Electronic Devices
Experimental Skills
JEE Mains Chemistry
Some Basic Concepts in Chemistry
Atomic Structure
Chemical Bonding and Molecular Structure
Chemical Thermodynamics
Solutions
Equilibrium
Redox Reactions and Electrochemistry
Chemical Kinetics
Classification of Elements and Periodicity
p-Block Elements
d-Block and f-Block Elements
Coordination Compounds
Purification and Characterisation of Organic Compounds
Some Basic Principles of Organic Chemistry
Hydrocarbons
Organic Compounds Containing Halogens
Organic Compounds Containing Oxygen
Organic Compounds Containing Nitrogen
Biomolecules
Practical Chemistry Principles
JEE Mains Mathematics
Integral Calculus
Application of Derivatives
Continuity and Differentiability
Sets, Relations, and Functions
Complex Numbers Quadratics
Matrices and Determinants
Permutations and Combinations
Binomial Theorem and Its Simple Applications
Sequence and Series
Limit, Continuity, and Differentiability
Differential Equations
Coordinate Geometry
Three Dimensional Geometry
Vector Algebra
Statistics and Probability
Trigonometry