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Mathematics - Sequences and Series

Practise 361 JEE Main previous year questions on Sequences and Series, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Sequences and Series has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 361 questions in all. 25% of them were easy, 48% moderate and 27% tough. Most of its questions came from 2023, with 46 questions that year. In the last three years (2024–2026) it had 83 questions across 49 papers, about 1.7 per paper.

The chapter's 8 topics are not weighted equally: Summation of Series (125 questions, 35%), Arithmetic Progression (110 questions, 30%), and Geometric Progression (62 questions, 17%) have been asked the most. Summation of Series has also led over the last five years, with 65 questions. Summation of Series has produced the most tough questions (70).

  1. 1Let upto 40 terms. If is a root of the equation , , then is equal to:08 Apr, 2026 (E)Arithmetic Progression
  2. 2The value of is:06 Apr, 2026 (M)Summation of Series
  3. 3The sum of the first ten terms of an A.P. is and the sum of the first two terms of a G.P. is . If the first term of the A.P. is equal to the06 Apr, 2026 (M)Mixed Question on AP and GP
  4. 4For the functions , and , , let . If the first term of a G.P. is , its common ratio is and the sum of its first terms is , , then is equal t06 Apr, 2026 (M)Geometric Progression
  5. 5The sum upto 10 terms is equal to :06 Apr, 2026 (E)Summation of Series
  6. 6Let the sum of the first terms of an A.P. be . Then the sum of squares of the first terms of the A.P. is:05 Apr, 2026 (M)Arithmetic Progression
  7. 7is equal to:05 Apr, 2026 (M)Summation of Series
  8. 8If the sum of the first terms of the series is , , then is equal to :05 Apr, 2026 (E)Summation of Series
  9. 9Let be arithmetic means between the numbers and . Then the mean of and is equal to :05 Apr, 2026 (E)Arithmetic Progression
  10. 10The first term of an A.P. of non-negative terms is . If the sum of this A.P. is the cube of its last term, then its common difference is:04 Apr, 2026 (M)Arithmetic Progression
  11. 11Let and . Then the value of is equal to:04 Apr, 2026 (E)Geometric Progression
  12. 12Let , be the roots of the quadratic equation for some . Then is equal to :02 Apr, 2026 (M)Summation of Series
  13. 13Let be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let be the set of first 71 terms of a02 Apr, 2026 (M)Arithmetic Progression
  14. 14If , then is equal to _______.02 Apr, 2026 (M)Summation of Series
  15. 15Let be an A.P. and be an increasing G.P. If and , then is equal to:02 Apr, 2026 (E)Arithmetic Progression
  16. 16The sum up to 8 terms, is:02 Apr, 2026 (E)Summation of Series
  17. 17The common difference of the A.P.: is 13 more than the common difference of the A.P.: . If and , then is equal to28 Jan, 2026 (M)Arithmetic Progression
  18. 18The value of is28 Jan, 2026 (M)Summation of Series
  19. 19In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is , then i28 Jan, 2026 (M)Geometric Progression
  20. 20Let the arithmetic mean of and be . If is such that are in A.P., then the equation has:28 Jan, 2026 (E)Arithmetic Progression
  21. 21is equal to :28 Jan, 2026 (E)Geometric Progression
  22. 22If , where and are positive integers such that , then is equal to 。28 Jan, 2026 (E)Summation of Series
  23. 23Consider an A.P.: . If , and , then is equal to24 Jan, 2026 (M)Arithmetic Progression
  24. 24Let be a sequence and denote the product of the first terms of this sequence. If and , then is equal to24 Jan, 2026 (M)Geometric Progression
  25. 25Let be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If and , then the largest term of the A24 Jan, 2026 (E)Arithmetic Progression
  26. 26upto infinite terms, is equal to24 Jan, 2026 (E)Geometric Progression
  27. 27Let . If and , then is equal to23 Jan, 2026 (E)Arithmetic Progression
  28. 28If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is22 Jan, 2026 (M)Arithmetic Progression
  29. 29Suppose are in A.P. and are in G.P. If and , then is equal to .22 Jan, 2026 (E)Mixed Question on AP and GP
  30. 30Let be G.P. of increasing positive terms such that and . Then is equal to :21 Jan, 2026 (M)Geometric Progression
  31. 31Let and for . Then is equal to .21 Jan, 2026 (M)Summation of Series
  32. 32The positive integer n, for which the solutions of the equation are two consecutive even integers, is :21 Jan, 2026 (E)Summation of Series
  33. 33Let be a G.P. of common ratio . If , then is equal to :21 Jan, 2026 (E)Geometric Progression
  34. 34then is equal to08 Apr, 2025 (E)Summation of Series
  35. 35Let be in a geometric progression. are subtracted respectively from then the resulting numbers are in an arithmetic progression. Then the va07 Apr, 2025 (M)Geometric Progression
  36. 36Let be the term of an A. P. If and , then is equal to :07 Apr, 2025 (E)Arithmetic Progression
  37. 37If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15307 Apr, 2025 (E)Geometric Progression
  38. 38upto 40 terms is equal to04 Apr, 2025 (M)Summation of Series
  39. 39Let and be the sets consisting of the first 2025 terms of two arithmetic progressions. Then is04 Apr, 2025 (M)Arithmetic Progression
  40. 40Consider two sets and , each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and 04 Apr, 2025 (E)Arithmetic Progression
  41. 41If the sum of the first 20 terms of the series is , where and are coprime, then is equal to :-04 Apr, 2025 (E)Summation of Series
  42. 42Let be a G. P. of increasing positive numbers. If and , then is equal to03 Apr, 2025 (M)Geometric Progression
  43. 43The sum . upto 20 terms, is equal to03 Apr, 2025 (M)Summation of Series
  44. 44The sum upto terms, is equal to03 Apr, 2025 (E)Summation of Series
  45. 45Let be in an A.P. such that . If , then n is:02 Apr, 2025 (M)Arithmetic Progression
  46. 46The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds t02 Apr, 2025 (E)Arithmetic Progression
  47. 47If the sum of the first 10 terms of the series is , where , then is equal to______02 Apr, 2025 (E)Summation of Series
  48. 48Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and29 Jan, 2025 (M)Arithmetic Progression
  49. 49The value of \( _{n } ( _{k=1}^n {k^3+6 k^2+11 k+5}{(k+3)!} )\) is:29 Jan, 2025 (M)Summation of Series
  50. 50Let be an Arithmetic Progression such that . Then is equal to _______29 Jan, 2025 (E)Arithmetic Progression

Frequently Asked Questions

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

This chapter includes 361 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

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

Sequences and Series has appeared in 25 of the 25 years of JEE Main papers covered here, with 361 questions across 196 papers - about 2 per paper it appears in.

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

Of the 361 questions analysed for this chapter, 25% are easy, 48% moderate and 27% tough. 2023 had the most, with 46 questions.

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

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

  • Summation of Series - 125 questions (35%)
  • Arithmetic Progression - 110 questions (30%)
  • Geometric Progression - 62 questions (17%)
  • Summation of Series has produced the most tough questions (70).
6.Is Sequences and Series's weightage in JEE Main going up or down?

Across all 196 papers analysed, Sequences and Series has averaged about 1.8 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.