Sequence and Series JEE Questions With Solution PDF, Practice Now

Sequence and Series JEE Questions: Sequence and Series an important topics for competitive exam aspirants, such as JEE Main and JEE Advanced. In the sequence and series, we learn how numbers are arranged in a specific order and follow a rule to generate a sequence. There are different types of sequence patterns that help in solving various types of problems by using formulas and logic.

Questions based on sequences and series are asked in JEE Main and Advanced every year. It tests a student’s understanding of the structure of a number series or the next term of the series using the sequence rule. It is not only useful for the Mathematics section but also helps to build analytical thinking, which can be applied to other topics as well.

Sequence and Series JEE Questions Overview

The JEE exam includes approximately 12 – 13 questions from Sequence and Series. The topics include Arithmetic Progression (AP), Geometric Progression (GP), Harmonic Progression (HP), General term, and special series (Sum of squares, Sum of cubes, etc).

Some questions are also given based on a series of functions, telescoping series or based on mixed series. Such questions in the JEE Sequence and Series chapter help the examiner check if the student knows to identify patterns and use the relevant formula.

The JEE Advanced sequence questions may also sometimes be slightly more challenging. The problems may include combinations of different sequences or sequences with the application of higher-level logic. There may also be questions that include concepts from other chapters (functions or algebra, for example) mixed with sequence and series concepts.

That is why, students must prepare not only the formulas but also the solving of conceptual questions. A strong understanding of the basics and regular solving of sequence and series questions for JEE will help a student score well in the Mains as well as the Advanced exam.

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Important Sequence and Series JEE Questions

Below are some important questions of sequence and series for JEE which students should practice regularly. Each question helps build understanding step-by-step.

Q1. Let a_n be the n-th term of an arithmetic progression. If ∑(r=1)^100 2a_r = α and ∑(r=1)^100 a_r = β, the common difference of the A.P. is:

1. α - β

2.  β - α

3.  (α - β) / 2

4.  None of these

Q2. The series of natural numbers is divided into groups (1, 2, 3, 4), (5, 6, 7, 8, 9), and so on. The sum of the numbers in the n-th group is:

1. n³ + n

2.  (n-1)³ + n³

3.  n³ + 1 + (n-1)³

4. (n+1)³ + (n-1)³

Q3. The arithmetic mean of two numbers is 18/3 and the positive square root of their product is 15. The larger of the two numbers is:

1. 24

2. 25

3. 20

4. 30

Q4. If sec(α - 2β), sec(α + 2β) are in arithmetic progression, then cos α = cos β. The value of λ is:

1. 1

2.  ½

3.  3

4.  1/2

Q5. If S, P, R are the sum, product, and sum of the reciprocals, respectively of n terms in an increasing G.P., and Sⁿ = Rⁿ = Pᵏ, then k is equal to:

1. 1

2.  2

3. 3

4. None of these

Q6. If the sum to infinity of the series 1 + 4x + 7x² + 10x³ + ... is 35/16, then x equals to:

1. 19/7

2. ⅕

3. ¼

4. None of these

Q7. If 1 / (√b + √c), 1 / (√c + √a), 1 / (√a + √b) are in A.P., then:

1. G.P.

2. G.P. only if x < 0

3. G.P. only if x > 0

4. None of these

Q8. If a₁, a₂, a₃, a₄ are four positive real numbers, then the minimum value of ∑ aᵢ / aⱼ, where i, j ∈ {1, 2, 3, 4}, i ≠ j is:

1. 6

2. 8

3. 12

4. 24

Q9. If a₁, a₂, a₃, a₄, a₅ are in H.P., then:

1. a₁a₂ + a₃a₄ + a₅a₁ = 4a₁a₅

2.  3a₁a₃ = 4a₄a₅

3.  4a₁a₃ = 4a₄a₅

4.  a₁ + a₂ + a₃ + a₄ = 4

Q10. If a₁, a₂, a₃, ..., aₙ are in HP and f(K) = ∑ aᵢ - aₖ, then:

1. a₁, a₂, aₙ are in G.P.

2.  a₁, a₂, aₙ are in HP.

3.  a₁, a₂, aₙ are in AGP.

4.  a₁, a₂, aₙ are in AP.

Q11. If the roots of the equation 10x³ - Kx² - 54x - 27 = 0 are in HP, then K is equal to:

1. 3

2. 6

3. 9

4. 12

Q12. If a, b, c are in H.P., then the value of a³b³ + b³c³ + c³a³ is:

1. 9ac - 6b²

2.  3ac - 2b²

3.  9ac - 4b²

4.  9ac - 2b²

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Sequence and Series JEE Questions PDF with Solution

PW provides a detailed PDF that includes all the important sequence and series questions for JEE. This PDF has questions from the basic to the advanced level. It also has solutions explained in a simple step-by-step manner so that every student can understand the method clearly.

For the JEE or JEE Advanced aspirants preparing for the JEE 2026 exam, it is recommended to revise the below PDF at least twice. Practice all types of questions mentioned in the PDF, verify your answers, and go through the easy tricks adopted for the solutions. This will ensure you have a firm grasp of the entire chapter and clear confidence to perform better in the actual exam.