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Mathematics - Sequences and Series

Practise 61 WBJEE previous year questions on Sequences and Series, compiled from papers spanning 2009 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 WBJEE tests.

Sequences and Series has been asked in 18 of the 18 years of WBJEE papers analysed (2009–2026), with 61 questions in all. 25% of them were easy, 56% moderate and 20% tough. Most of its questions came from 2013, with 8 questions that year. In the last three years (2024–2026) it had 8 questions across 3 papers, about 2.7 per paper.

The chapter's 9 topics are not weighted equally: Arithmetic Progression (13 questions, 21%), Geometric Progression (13 questions, 21%), and Summation of Series (11 questions, 18%) have been asked the most. Arithmetic Progression has also led over the last five years, with 4 questions. Summation of Series has produced the most tough questions (5).

  1. 1If , then is equal to2026Infinite Series
  2. 2If denotes the term of an A.P. and , then which one of the following options is a root of the equation ?2026Arithmetic Progression
  3. 3Let are in G.P. such that and . If , then is2026Geometric Progression
  4. 4The quantities form an infinite decreasing G.P. If , then the common ratio of the progression for which the expression is at a maximum is2026Geometric Progression
  5. 5If the sum of ' ' terms of an A.P. is and its th term is 164 , then the value of is2025Summation of Series
  6. 6The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112 . If its first term is 11 , then 2025Arithmetic Progression
  7. 7If for the series . etc, bears a constant ratio with then . are in2024Harmonic Progression
  8. 8Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If and be the term of A.P. an2024Mixed Question on AP and GP
  9. 9If the \(n\) terms \(a_1, a_2, . ., a_n\) are in A.P. with increment \(r\), then the difference between the mean of their squares & the squa2023Arithmetic Progression
  10. 10If \(1, _9 (3^{1-x}+2 ), _3 (4.3^{ {x}}-1 )\) are in A.P, then \(x\) equals2023Arithmetic Progression
  11. 11Consider a quadratic equation \(a x^2+2 b x+c=0\) where \(a, b, c\) are positive real numbers. If the equation has no real root, then which 2023Harmonic Progression
  12. 12Let \(a_1, a_2, a_3, , a_n\) be positive real numbers. Then the minimum value of \( {a_1}{a_2}+ {a_2}{a_3}+ .+ {a_n}{a_1}\) is2023Inequalities
  13. 13The value of \( _{n } [ ( {1}{2 3}+ {1}{2^2 3} )+ ( {1}{2^2 3^2}+ {1}{2^3 3^2} )+ + ( {1}{2^n 3^n}+ {1}{2^{n+1} 3^n} ) ]\) is2023Geometric Progression
  14. 14Let and . Then2022Inequalities
  15. 15If are in G. P. and are in A. P., then are the lengths of the sides of a triangle which is2022Mixed Question on AP and GP
  16. 16If , then the maximum value of is given by2022Inequalities
  17. 17Consider the real valued function such that and satisfying for every Then the value of is2021Arithmetic Progression
  18. 18Let be real numbers, each greater than 1 , such that . If the value of is 9 , then the value of ' ' must be2021Means
  19. 19Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while are in A.P. Then are the lengths of the sides of2021Mixed Question on AP and GP
  20. 20If and are arbitrary positive real numbers, then the least possible value of is2020Inequalities
  21. 21Let for all , then2020Inequalities
  22. 22The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be and , then tan and tan are2019Geometric Progression
  23. 23A particle starts at the origin and moves l unit horizontally to the right and reaches , then it moves unit vertically up and 2 reaches , th2019Geometric Progression
  24. 24Given that numbers of arithmetic means are inserted between two sets of numbers and where . Suppose further that the mih means between these2018Arithmetic Progression
  25. 25In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is2017Geometric Progression
  26. 26If is a positive real number different from 1 such that are in , then2016Arithmetic Progression
  27. 27If are real numbers and then is equal to2016Summation of Series
  28. 28The sum of terms of the following series is2016Summation of Series
  29. 29If is an imaginary cube root of unity, then the value of is2016Summation of Series
  30. 30If the first and th terms of an , GP and are equal and their th terms are respectively then always2016Inequalities
  31. 31Let denotes the number of divisors of including 1 and itself. Then, and are2015Geometric Progression
  32. 32Let . Then, the number of real values of for which the three unequal terms are in is2014Harmonic Progression
  33. 33Let denote the sum of the infinite series Then2014Summation of Series
  34. 34The minimum value of is2014Mixed Question on AP and GP
  35. 35Five numbers are in HP. The middle term is 1 and the ratio of the second and the fourth terms is 2: 1 . Then, the sum of the first three ter2013Harmonic Progression
  36. 36If and are in , then the straight line will always pass through a fixed point whose coordinates are2013Arithmetic Progression
  37. 37The value of is2013Summation of Series
  38. 38Six positive numbers are in GP, such that their product is 1000 . If the fourth term is 1 , then the last term is2013Geometric Progression
  39. 39Five numbers are in AP with common difference If the 1 st, 3 rd and 4 th terms are in GP, then2013Mixed Question on AP and GP
  40. 40Let be such that is injective and for all if and are in then and are in2013Arithmetic Progression
  41. 41If and then2013Arithmetic Geometric Progression
  42. 42The value of the infinite series2013Summation of Series
  43. 43Let the coefficients of powers of in the , 3rd and 4 th terms in the expansion of where is a positive integer, be in arithmetic progression.2012Arithmetic Progression
  44. 44The sum ! equals2012Summation of Series
  45. 45Six numbers are in AP such that their sum is 3 . The first term is 4 times the third term. Then, the fifth term is2012Arithmetic Progression
  46. 46The sum of the infinite series is equal to2012Geometric Progression
  47. 47If 64,27,36 are the Pth th and th terms of a GP, then is equal to2012Geometric Progression
  48. 48Let \(a, b, c, p, q\) and \(r\) be positive real numbers such that \(a, b\) and \(c\) are in GP and \(a^{p}=b^{q}=c^{r}\). Then,2012Geometric Progression
  49. 49Let be the sum of an infinite GP series whose first term is and common ratio is Then, the value of is equal to2012Geometric Progression
  50. 50The coefficient of \(x^n\) in the expansion of \( {e^{7 x}+e^x}{e^{3 x}}\) is2011Summation of Series

Frequently Asked Questions

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

This chapter includes 61 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Sequences and Series has appeared in 18 of the 18 years of WBJEE papers covered here, with 61 questions across 18 papers - about 3 per paper it appears in.

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

Of the 61 questions analysed for this chapter, 25% are easy, 56% moderate and 20% tough. 2013 had the most, with 8 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 - 13 questions (21%)
  • Geometric Progression - 13 questions (21%)
  • Summation of Series - 11 questions (18%)
  • Summation of Series has produced the most tough questions (5).
6.Is Sequences and Series's weightage in WBJEE going up or down?

Across all 18 papers analysed, Sequences and Series has averaged about 3.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.