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Mathematics - Sequences and Series

Practise 118 NTA Abhyas (JEE Main) questions on Sequences and Series. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Sequences and Series has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 118 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let a n = 16 , 4 , 1 , … … be a geometric sequence. The value of ∑ n = 1 ∞ P n n , where P n is the product of the first n terms, is equal t
  2. 2The sum of the infinite series 1 3 + 3 3.7 + 5 3.7 . 11 + 7 3.7 . 11.15 + . . . . . . . is
  3. 3Let l , m and n are three distinct numbers in arithmetic progression. Also l 2 , m 2 and n 2 are in geometric progression and l + m + n = 3
  4. 4If 1 2020 + 2 2019 + 3 2018 + . . . . . . . . . + 2020 1 = 2020 × 2021 × k , then the value of k 100 is equal to
  5. 5If 2 , 7 , 9 and 5 are subtracted respectively from four numbers in geometric progression, then the resulting numbers are in arithmetic prog
  6. 6The least positive term of an arithmetic progression whose first two terms are 5 2 and 23 12 is
  7. 7If S = 1 25 + 2 24 + 3 23 + . . . . . . + 24 2 + 25 1 , then the value of S 900 is equal to
  8. 8The sum of 50 terms of the series 3 + 7 + 13 + 21 + 31 + 43 + . . . . . is equal to S 50 , then the value of S 50 12500 is
  9. 9Let , and be the roots of the equation x 3 + 6 x 2 - p x - 42 = 0 . If , and are in arithmetic progression then + + =
  10. 10The second term of an infinite geometric progression is 2 and its sum to infinity is 8 . The first term is
  11. 11The 5 th and the 31 s t terms of an arithmetic progression are, respectively 1 and 77 . If the K t h term of the given arithmetic progressio
  12. 12The sum of four numbers in an arithmetic progression is 48 and the ratio of the product of the extremes to the product of the two middle ter
  13. 13The sum of the first 10 terms of the series 5 1 ⋅ 2 ⋅ 3 + 7 2 ⋅ 3 ⋅ 9 + 9 3 ⋅ 4 ⋅ 27 + . . . . is
  14. 14If S = ∑ r = 1 80 r r 4 + r 2 + 1 , then the value of 6481 S 1000 is
  15. 15If 5 2 5 4 5 6 … . 5 2 n = 0.04 - 28 , then the value of n is equal to
  16. 16Let a , b , c and d are in a geometric progression such that a b c d , a + d = 112 and b + c = 48 . If the geometric progression is continue
  17. 17If a 1 and b 1 , then the sum of the series a a + b + a 2 a 2 + b 2 + a 3 a 3 + b 3 + is
  18. 18The sum to the infinite terms of the series 5 3 2 ⋅ 7 2 + 9 7 2 ⋅ 1 1 2 + 13 1 1 2 ⋅ 1 5 2 + . . . . is
  19. 19If log 2 ⁡ 5 2 x + 1 , log 4 ⁡ 2 1 - x + 1 and 1 are in arithmetic progression, then x is equal to
  20. 20Sum to n terms of the series 1 4 1.3 + 2 4 3.5 + 3 4 5.7 + . . . . . is equal to
  21. 21The sum to 10 terms of the series 1 + 2 1.1 + 3 1.1 2 + 4 1.1 3 + . . . . is
  22. 22If 2 , h 1 , h 2 , . . . . . , h 20 , 6 are in harmonic progression and 2 , a 1 , a 2 , . . . . , a 20 , 6 are in arithmetic progression, th
  23. 23If a 1 + a 5 + a 10 + a 15 + a 20 + a 24 = 225 , then the sum of the first 24 terms of the arithmetic progression a 1 , a 2 , a 3 . . . . .
  24. 24The sum of the series 2 1 · 2 + 5 2 · 3 · 2 + 10 3 · 4 · 2 2 + 17 4 · 5 · 2 3 + ...... to n terms is
  25. 25Let α and β are two positive roots of x 2 - 2 a x + a b = 0 where 0 b a , then the value of S n = 1 + 2 b a + 3 b a 2 + . . . . . + n b a n
  26. 26If the lengths of the sides of a right-angled triangle A B C , right angled at C , are in arithmetic progression, then the value of 5 sin A
  27. 27The arithmetic mean of two positive numbers a and b exceeds their geometric mean by 3 2 and the geometric mean exceeds their harmonic mean b
  28. 28Given and are the roots of the quadratic equation x 2 - 4 x + k = 0 k 0 . If , 2 + 2 and 3 + 3 are in geometric progression, then the value
  29. 29If 1, log 3 3 1 - x + 2 , log 3 4.3 x - 1 are in arithmetic progression, then x equals
  30. 30In an arithmetic progression containing 99 terms, the sum of all the odd numbered terms is 2550 . If the sum of all the 99 terms of the arit
  31. 31The sum of an infinite geometric progression is 5 4 times the sum of all the odd terms. If the first term is non-zero, then the common ratio
  32. 32The sum ∑ r = 1 50 r ⋅ 2 r + 2 50 - r is equal to
  33. 33In an increasing geometric progression, the sum of the first and the last term is 99 , the product of the second and the last but one term i
  34. 34For the series S = 1 + 1 1 + 3 1 + 2 2 + 1 1 + 3 + 5 1 + 2 + 3 2 + 1 1 + 3 + 5 + 7 1 + 2 + 3 + 4 2 + . . . . . , if the 7 t h term is K , th
  35. 35If ln ⁡ 2 x 2 - 5 , ln ⁡ x 2 - 1 and ln ⁡ x 2 - 3 are the first three terms of an arithmetic progression, then its fourth term is
  36. 36Let α and β be two numbers where α β . The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the
  37. 37If the sum of the first 100 terms of an arithmetic progression is - 1 and the sum of the even terms lying in the first 100 terms is 1 , then
  38. 38Sum of the first hundred numbers common to the two arithmetic progressions 12,15,18 , … … … and 17 , 21 , 25 , … … . . is
  39. 39The sum of infinitely many terms of a geometric progression is 3 times the sum of even terms. If the first term is non-zero, then the common
  40. 40If Σ k = 1 ∞ 1 k + 2 k + k k + 2 = a + b c , where a , b , c ∈ N and a , b , c ∈ [ 1 , 15 ] , then a + b + c is equal to
  41. 41Let the sets A = 2 , 4 , 6,8 … and B = 3 , 6 , 9 , 12 … such that n A = 200 and n B = 250. If n A ∪ B = k , then k 100 is equal to
  42. 42If the sum to infinity of the series 1 + 4 x + 7 x 2 + 10 x 3 + . … … . is 35 16 , where x 1 , then x is equal to
  43. 43Let α , β and γ are the roots of the equation 2 x 3 + 9 x 2 - 27 x - 54 = 0 . If α , β , γ are in geometric progression, then the value of α
  44. 44For the series S = 1 + 1 1 + 3 1 + 2 2 + 1 1 + 3 + 5 1 + 2 + 3 2 + 1 1 + 3 + 5 + 7 1 + 2 + 3 + 4 2 + . , if the sum of the first 10 terms is
  45. 45If 17 arithmetic means are inserted between 7 2 and - 83 2 , then the 17 t h arithmetic mean is
  46. 46The sum to n terms of 1 1.3 + 2 1.3 . 5 + 3 1.3 . 5.7 + 4 1.3 . 5.7 . 9 + . . . . . . . . is
  47. 47If S = ∑ n = 1 9999 1 n + n + 1 n 4 + n + 1 4 , then the value of S is equal to
  48. 48There are n sets of observations given as 1 , 2 ,3 , 4 ,5 , 6 , 7 ,8 , 9 ,10 , . . . . . The mean of the 1 3 t h set of observations is equa
  49. 49If the sum of the series 1 + 3 2 + 5 4 + 7 8 + . . . . + 2 n - 1 2 n - 1 is f n , then the value of f 8 is
  50. 50If the 2 n d , 5 t h and 9 t h terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this ge

Frequently Asked Questions

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

This chapter includes 118 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Sequences and Series questions in NTA Abhyas (JEE Main)?

Of the 118 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.