Sequence and Series is among the most repeated topic in the JEE Advanced 2025 syllabus (Mathematics). Over the past 10 years, concept sequences include Arithmetic, Geometric, Harmonic Sequences, and Fibonacci numbers have been consistently asked in the JEE Advanced exam.
Must Read Articles:
- Download JEE Advanced Last 10 year PYQ for Free
- Download JEE 2024 Question Paper with Detailed Solutions
Most important Topics for JEE Advanced 2025 (Sequence and Series):
Based on the JEE Advanced previous year paper trends, the following are the high-weightage topics in JEE Advanced 2025:
- Sequences
- Arithmetic Mean
- Geometric Mean
- Arithmetic progression
- Geometric Progression
- Harmonic Progression
- Sum up to n terms
- Arithmetic-geometric series
JEE Advanced previous year question papers and mock tests can assist IIT Aspirants to achieve higher rankings in JEE Advanced 2025.
Listed below the most repeated questions JEE Advanced Previous Year Questions (PYQs) for Sequence and Series along with detailed solutions
Question 1:
Let a1,a2,a3,…… be an arithmetic progression with a1=7 and common difference 8 .Let T1,T2,T3,.… be such that T1=3 and Tn+1−Tn=an for n≥1 Then, which of the following is/are TRUE ?
Question 2:
Question 3:
For any positive integer n, let Sn:(0,∞)→R be defined by
Question 4 :
Let M={(x,y)∈R×R:x2+y2≤r2},
Consider M with r=513/1025 Let k be the number of all those circles
Cn that are inside M. Let 1 be the maximum possible number of circles among these k circles such that no two circles intersect Then
- k+2l=22
- 2k+1=26
- 2k+3l=34
- 3k+2l=40
Question 5:
Let a1,a2,a3,…… be a sequence of positive integers in arithmetic progression with common difference 2 Also, let b1,b2,b3,…… be a sequence of positive integers in geometric progression with common ratio 2 .If a1=b1=c, then the number of all possible values of c, for which the equality 2(a1+a2+…+an)=b1+b2+…+bn holds for some positive integer
n, is
Question 6:
If a1,a2,a3,...... are in harmonic progression with a1=5 and a20=25. Then, the least positive integer n for which an<0, is
- 22
- 23
- 24
- 25
Question 7:
Let f(x)=ax2+bx+c,a≠0 and Δ=b2−4ac. If a+β, a2+β2 and a3+β3 are in GP, then
- Δ=0
- bΔ=0
- cΔ=0
- bc≠0
Question 8:
An infinite GP has first term x and sum 5, then x belongs to
- x < - 10
- -10 < x < 0
- 0 < x < 10
- x > 10
Question 9:
- 2tana
- 1
- 2
- sec2a
Question 10:
If the positive numbers a,b,c,d are in AP. Then, abc,abd,acd,bcd are
- not in AP/GP/HP
- in AP
- in GP
- in HP
Question 11:
Let α,β be the roots of x2−x+p=0 and y,δ be the roots of x2−4x+q=0 if α,β,yδ are in GP, then the integer values of p and q respectively are
- -2,-32
- -2,3
- -6,3
- -6,-32
Question 12:
Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 then
- a = 4/7, r = 3/7
- a = 2, r = 3/8
- a = 3/2, r = 1/2
- a = 3, r = 1/4
Question 13:
If a,b,c,d are positive real numbers such that a+b+c+d=2, then M=(a+b)(c+d) satisfies the relation.
- 0
- 1<M≤2
- 2≤M≤3
- 3≤M≤4
Question 14:
The harmonic mean of the roots of the equation
(5+2)x2−(4+5)x+8+25=0 is
- 2
- 4
- 6
- 8
Question 15:
Let a1,a2,...,a10 be in AP and h1,h2 equal to .....,h10 be in HP. If a1=h1=2 and a10=h10=3, then a4h7 is
- 2
- 3
- 5
- 6
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination was conducted ONLY in the Computer Based Test (CBT) mode.
- Number of papers: Two question papers: Paper 1 and Paper 2 of three hours duration each. Both papers are compulsory.
- Language: English and Hindi
- Total duration: 6 hours
- Number of sections: Each question paper consisted of three separate sections, viz., Physics, Chemistry and Mathematics.
- Marking scheme: Details of the marking scheme were provided in the “Instructions to Candidates” section at the time of examination. The same is also explained further below.
JEE Advanced 2025 Mathematics Syllabus
JEE Advanced Mathematics Syllabus consists of nine units- Sets, Relations and Functions ; Algebra ; Matrices; Probability and Statistics; Trignometry; Analytical Geometry; Differential Calculus ; Integral Calculus and Vectors. Check JEE Advanced 2025 Syllabus
JEE Advanced Mathematics Syllabus according to the seven units is defined below.
| Units | Sub Units |
|---|---|
| Sets, Relations, and Functions | - Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for finite number of sets), and practical problems based on them.- Cartesian product of finite sets, ordered pair, relations, domain, and codomain of relations, equivalence relation.- Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions. |
| Algebra | - Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.- Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.- Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.- Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients. |
| Matrices | - Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | - Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.- Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. |
| Trigonometry | - Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.- Inverse trigonometric functions (principal value only) and their elementary properties. |
| Analytical Geometry | - Topics related to coordinate geometry, straight lines, circles, conic sections, and other geometric properties. |
| Differential Calculus | - Concepts of limits, continuity, differentiation, derivatives of functions, application of derivatives, increasing and decreasing functions, maxima and minima. |
| Integral Calculus | - Indefinite and definite integrals, properties of integrals, fundamental theorem of calculus, methods of integration, applications of integration. |
| Vectors | - Vectors and their properties, operations on vectors, scalar and vector products, applications in geometry and physics. |
JEE Advanced Mathematics Chapter-wise Weightage
However, based on the previous year's analysis, the chapters along with the number of questions and marks tabulated below:
| Chapter Name | Number of Questions | Marks |
|---|---|---|
| Application of Derivatives | 3 | 9 |
| Ellipse | 1 | 3 |
| Circles | 2 | 6 |
| Parabola | 2 | 7 |
| Definite Integral | 2 | 7 |
| Permutations and Combinations | 1 | 3 |
| Sequence and Series | 1 | 3 |
| Matrices | 2 | 7 |
| Limit and Continuity | 1 | 4 |
| Probability | 1 | 4 |
| Complex Numbers | 1 | 4 |
| Hyperbola | 1 | 4 |
JEE Advanced - Marks wise Weightage of Topics
| Topics | Marks |
|---|---|
| Calculus | 40-50 marks |
| Vector and 3D Geometry | 15-20 marks |
| Probability & Permutation & Combination | 15-20 marks |
| Parabola, Hyperbola, Ellipse, Rectangular Hyperbola | 15 marks |
| Complex Numbers | 15 marks |
Important Books for Mathematics:
JEE Advanced 2024 Question Paper PDF with Solutions
| Paper Name | Question Paper Link | Solutions Link |
|---|---|---|
| JEE Advanced 2024 Paper 1 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 2 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
JEE Advanced Last 5 Year Mathematics Papers Pdf
Download free JEE Advanced Previous Year Question Paper PDFs from the table provided below:-
| JEE Advanced Paper Name | Question Paper Link |
|---|---|
| JEE Advanced 2024 Question Paper PDF | Click Here |
| JEE Advanced 2023 Question Paper PDF | Click Here |
| JEE Advanced 2022 Question Paper PDF | Click Here |
| JEE Advanced 2021 Question Paper PDF | Click Here |
| JEE Advanced 2020 Question Paper PDF | Click Here |
| JEE Advanced 2019 Question Paper PDF | Click Here |
| JEE Advanced 2018 Question Paper PDF | Click Here |
| JEE Advanced 2017 Question Paper PDF | Click Here |
| JEE Advanced 2016 Question Paper PDF | Click Here |
JEE Advanced 2023 Question Paper PDF Download With Solutions
| Paper | Question Paper PDF | Answer Key PDF |
|---|---|---|
| Question Paper 1 PDF | Download PDF | Check Solutions |
| Question Paper 2 PDF | Download PDF | Check Solutions |
| Question Paper AAT PDF | Download PDF | Check Solutions |
JEE Advanced 2022 Question Paper
| 2022 Question Paper | PDF Download |
|---|---|
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
JEE Advanced 2021 Question Paper
| Question Paper | PDF Download | ||
|---|---|---|---|
| Question Paper 1 PDF | Physics | Chemistry | Maths |
| Question Paper 2 PDF | Physics | Chemistry | Maths |
JEE Advanced 2020 Question Paper
| Question Paper | PDF Download |
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
Frequently Asked Questions
Q1. Is sequence and series important for JEE Advanced exam?
Yes, Sequence and series is an important topic for JEE Advanced and 1-2 questions asked from arithmetic, geometric and harmonic mean frequently asked in the exam. Mastering this topic of series will fetch you good marks.
Q2. Which is the highest-scoring subject in JEE Advanced?
The highest scoring subject in JEE Advanced may differ from person to person based on strengths, but most of the time Mathematics is one of the most scoring subjects. Topics of Probability like conditional probability, Definite integration and 3D geometry have heavy weightage. These are all calculation-based concepts, so with frequent practice, it is easy for students to get good marks.
Q3. What is a safe score for JEE Advanced IIT?
Fundamentally safe score in JEE Advanced 2025 is reliant, on difficulty level and cutoff patterns. In general, 40-50% of total marks can fetch a rank within the IIT admission category. For any top IITs (IIT Bombay, IIT Delhi, IIT Madras), a rank below 2500 is desired. Monitor the category-wise cutoff patterns and last year JEE Advanced cutoffs.
Q4. What is the difficulty level of JEE Advanced?
JEE Advanced is particularly famous for being of high difficulty, challenging conceptual clarity, application-based solving of problems, and time management. The mathematics part includes higher-order algebra, calculus, and coordinate geometry; physics demands an understanding of electromagnetism, mechanics, and modern physics at a deeper level; and chemistry has a combination of organic reaction mechanisms, physical chemistry calculations, and inorganic memorization. The test aims to check critical thinking and the application of multiple concepts.
Comments