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Mathematics - Sequences and Series

Practise 32 JEE Advanced previous year questions on Sequences and Series, compiled from papers spanning 2006 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Sequences and Series has been asked in 19 of the 27 years of JEE Advanced papers analysed (2000–2026), with 32 questions in all. 22% of them were easy, 50% moderate and 28% tough. Most of its questions came from 2007, with 6 questions that year. In the last three years (2024–2026) it had 1 question across 6 papers, about 0.2 per paper.

The chapter's 7 topics are not weighted equally: Arithmetic Progression (10 questions, 31%), Mixed Question on AP and GP (6 questions, 19%), and Summation of Series (5 questions, 16%) have been asked the most. Arithmetic Progression has also led over the last five years, with 2 questions. Summation of Series has produced the most tough questions (4).

  1. 1Let denote the set of all real numbers. Let be a function such that for all , and for all . Let the real numbers be in an arithmetic progres2025 (Paper 1)Arithmetic Progression
  2. 2Let 7 5 5 7 r denote the r + 2 digit number where the first and the last digits are 7 and the remaining r digits are 5 . Consider the sum S 2023 (Paper 1)Geometric Progression
  3. 3Let l 1 , l 2 . . . l 100 be consecutive terms of an arithmetic progression with common difference d 1 , and let w 1 , w 2 , , w 100 be cons2022 (Paper 1)Arithmetic Progression
  4. 4Let a 1 , a 2 , a 3 , be an arithmetic progression with a 1 = 7 and common difference 8 . Let T 1 , T 2 , T 3 , be such that T 1 = 3 and T n2022 (Paper 1)Summation of Series
  5. 5Paragraph: Let , where Consider the geometric progression Let and, for , let denote the sum of the first terms of this progression. For , le2021 (Paper 2)Geometric Progression
  6. 6Paragraph: Let , where Consider the geometric progression Let and, for , let denote the sum of the first terms of this progression. For , le2021 (Paper 2)Geometric Progression
  7. 7Let m be the minimum possible value of log 3 3 y 1 + 3 y 2 + 3 y 3 , where y 1 , y 2 , y 3 are real numbers for which y 1 + y 2 + y 3 = 9 . 2020 (Paper 1)Inequalities
  8. 8Let a 1 , a 2 , a 3 , . . . . . . . . . be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let b 2020 (Paper 1)Mixed Question on AP and GP
  9. 9Let A P a ; d denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d 0 . If A P 1 ;2019 (Paper 1)Arithmetic Progression
  10. 10Let X be the set consisting of the first 2018 terms of the arithmetic progression 1,6 , 11 , , and Y be the set consisting of the first 20182018 (Paper 1)Arithmetic Progression
  11. 11The sides of a right-angled triangle are in arithmetic progression. If the triangle has area 24 square units, then what is the length of its2017 (Paper 1)Arithmetic Progression
  12. 12The value of k = 1 13 1 sin 4 + k - 1 6 sin 4 + k 6 is equal to2016 (Paper 2)Summation of Series
  13. 13Let b i 1 for i = 1 , 2 , . , 101 . Suppose log e b 1 , log e b 2 , . . , log e b 101 are in Arithmetic Progression (A.P.) with the common d2016 (Paper 2)Mixed Question on AP and GP
  14. 14Column I Column II ( A ) In R 2 , if the magnitude of the projection vector of the vector i ^ + j ^ on 3 i ^ + j ^ is 3 and if = 2 + 3 , the2015 (Paper 1)Means
  15. 15Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the 2015 (Paper 2)Arithmetic Progression
  16. 16Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is 2014 (Paper 1)Mixed Question on AP and GP
  17. 17Let S n = k = 1 4 n - 1 k k + 1 2 k 2 . Then S n can take value(s)2013 (Paper 1)Summation of Series
  18. 18A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the rem2013 (Paper 1)Mixed Question on AP and GP
  19. 19Let be in harmonic progression with and . The least positive integer for which is2012 (Paper 2)Harmonic Progression
  20. 20Let be an arithmetic progression with and , . For any integer with , let . If does not depend on , then is2011 (Paper 1)Arithmetic Progression
  21. 21The minimum value of the sum of real numbers and with is2011 (Paper 1)Inequalities
  22. 22Let , denote the sum of the infinite geometric series whose first term is and the common ratio is . Then the value of is2010 (Paper 1)Summation of Series
  23. 23Let be real numbers satisfying and for . If , then the value of is equal to2010 (Paper 2)Arithmetic Progression
  24. 24If the sum of first terms of an is , then the sum of squares of these terms is2009 (Paper 2)Summation of Series
  25. 25Suppose four distinct positive numbers and are in GP. Let , and . Statement 1 The numbers and are neither in AP nor in GP. Statement 2 The n2008 (Paper 2)Mixed Question on AP and GP
  26. 26Paragraph: Let denotes the sum of the first terms of an arithmetic progression whose first term is and the common difference is . Let and fo2007 (Paper 1)Arithmetic Progression
  27. 27Paragraph: Let denotes the sum of the first terms of an arithmetic progression whose first term is and the common difference is . Let and fo2007 (Paper 1)Mixed Question on AP and GP
  28. 28Paragraph: Let denotes the sum of the first terms of an arithmetic progression whose first term is and the common difference is . Let and fo2007 (Paper 1)Arithmetic Progression
  29. 29Paragraph: Let denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For , let and has arithme2007 (Paper 2)Means
  30. 30Paragraph: Let denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For , let and has arithme2007 (Paper 2)Means
  31. 31Paragraph: Let denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For , let and has arithme2007 (Paper 2)Means
  32. 32Let and . Find a least odd natural number , so that .2006Geometric Progression

Frequently Asked Questions

1.How many questions are available for Sequences and Series?

This chapter includes 32 questions compiled from JEE Advanced papers spanning 2006 to 2025.

2.Are these questions only from JEE Advanced, or from other exams too?

These are JEE Advanced questions specifically for the Sequences and Series chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Sequences and Series an important chapter for JEE Advanced Mathematics?

Sequences and Series has appeared in 19 of the 21 years of JEE Advanced papers covered here, with 32 questions across 22 papers - about one per paper it appears in.

4.What is the difficulty level of Sequences and Series questions in JEE Advanced?

Of the 32 questions analysed for this chapter, 22% are easy, 50% moderate and 28% tough. 2007 had the most, with 6 questions.

5.Which topics in Sequences and Series should I focus on?

These topics have carried the most weightage in Sequences and Series:

  • Arithmetic Progression - 10 questions (31%)
  • Mixed Question on AP and GP - 6 questions (19%)
  • Summation of Series - 5 questions (16%)
  • Summation of Series has produced the most tough questions (4).
6.Is Sequences and Series's weightage in JEE Advanced going up or down?

Across all 22 papers analysed, Sequences and Series has averaged about 1.5 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.