JEE Mathematics

Arithmetic Progression (AP): JEE Questions & Solutions

41 previous-year JEE Mathematics questions on Arithmetic Progression (AP), each with a worked step-by-step solution.

Basic

Previous-year questions

  1. 01If 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 isMCQMediumJEE 2026
  2. 02Suppose a, b, c are in A.P. and a², 2b², c² are in G.P. If a < b < c and a+b+c = 1, then 9(a²+b²+c²) is equal to.NVAMediumJEE 2026
  3. 03Σ_(k=1)ⁿ a_k = α n² + β n. a₁₀=59, a₆=7a₁. Find α+β.MCQMediumJEE 2026
  4. 04Consider an A.P. a₁,a₂,…,aₙ; a₁>0. If a₂-a₁=-3/4, aₙ=1/4a₁, and Σ_(i=1)ⁿ aᵢ=525/2, then Σ_(i=1)¹⁷ aᵢ is equal toMCQMediumJEE 2026
  5. 05Let a₁,a₂,a₃,a₄ be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a₁+a₂+a₃+a₄=48 and…MCQMediumJEE 2026
  6. 06The common difference of the A.P.: a₁, a₂, …, a_m is 13 more than the common difference of the A.P.: b₁, b₂, …, bₙ. If b₃₁ = -277, b₄₃ =…MCQEasyJEE 2026
  7. 07Let the arithmetic mean of 1/a and 1/b be 5/16, where a>2. If α is such that a,4,α,b are in A.P., then the equation α x²-ax+2(α-2b)=0 has:MCQMediumJEE 2026
  8. 08Suppose that the number of terms in an A.P. is 2k, k ∈ ℕ. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55,…MCQMediumJEE 2025
  9. 09If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum…MCQMediumJEE 2025
  10. 10The roots of the quadratic equation 3x² - px + q = 0 are the 10^th and 11^th terms of an arithmetic progression with common difference 3/2.…NVAMediumJEE 2025
  11. 11Let Sₙ = 1/2 + 1/6 + 1/12 + 1/20 + … up to n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p…MCQMediumJEE 2025
  12. 12In an arithmetic progression, if S₄₀ = 1030 and S₁₂ = 57, then S₃₀ - S₁₀ is equal to:MCQMediumJEE 2025
  13. 13Let T_r be the r^th term of an A.P. If for some m, T_m = 1/25, T₂₅ = 1/20 and 20Σ_(r=1)²⁵ T_r = 13, then 5m Σ_(r=m)^2m T_r is equal to:MCQMediumJEE 2025
  14. 14The interior angles of a polygon with n sides, are in an A.P. with common difference 6^°. If the largest interior angle of the polygon is…MCQMediumJEE 2025
  15. 15Consider 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 and…MCQMediumJEE 2025
  16. 16Let a₁, a₂, …, a₂₀₂₄ be an Arithmetic Progression such that a₁ + (a₅ + a₁₀ + a₁₅ + … + a₂₀₂₀) + a₂₀₂₄ = 2233. Then a₁ + a₂ + a₃ + … + a₂₀₂₄…NVAMediumJEE 2025
  17. 17Let a₁, a₂, a₃, … be in an A.P. such that Σ_(k=1)¹² a_(2k-1) = -72/5a₁, a₁ ≠ 0. If Σ_(k=1)ⁿ a_k = 0, then n is:MCQMediumJEE 2025
  18. 18The 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…MCQMediumJEE 2025
  19. 19Let A = {1, 6, 11, 16, …} and B = {9, 16, 23, 30, …} be the sets consisting of the first 2025 terms of two arithmetic progressions. Then…MCQMediumJEE 2025
  20. 20Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p,…MCQMediumJEE 2025
  21. 21Let aₙ be the n-th term of an A.P. If Sₙ = a₁ + a₂ + a₃ + … + aₙ = 700, a₆ = 7, and S₇ = 7, then aₙ is equal to:MCQMediumJEE 2025
  22. 22Number of common terms in sequences 4, 9, 14... up to 25th term and 3, 6, 9... up to 37th term:MCQMediumJEE 2024
  23. 23The 20^th term from the end of the progression 20, 19.25, 18.5, 17.75, …, -129.25 is:MCQEasyJEE 2024
  24. 24In an A.P., the sixth term a₆ = 2. If the product a₁ * a₄ * a₅ is maximized, the common difference of the A.P. is equal to:MCQMediumJEE 2024
  25. 25If log a, log b, log c are in an A.P. and log a - log 2b, log 2b - log 3c, log 3c - log a are also in an A.P., then a: b: c is equal to:MCQMediumJEE 2024
  26. 26Let Sₙ denote the sum of the first n terms in an arithmetic progression. If S₂₀ = 790 and S₁₀ = 145, then S₁₅ - S₅ is:MCQMediumJEE 2024
  27. 27Let Sₙ be the sum of the first n terms of an arithmetic progression 3, 7, 11, …. If n(n + 1)/(Σ S_k) < 42, then n equals:NVAMediumJEE 2024
  28. 28Let 2^nd, 8^th, and 44^th terms of a non-constant A.P. be respectively the 1^st, 2^nd, and 3^rd terms of a G.P. If the first term of the…MCQMediumJEE 2024
  29. 29Let S(n) denote the sum of the first n terms of an arithmetic progression. If S(10) = 390 and the ratio of the tenth and fifth terms is…MCQMediumJEE 2024
  30. 30Let three real numbers a, b, c be in arithmetic progression, and a + 1, b, c + 3 in geometric progression. If a > 10 and their arithmetic…MCQMediumJEE 2024
  31. 31A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of…MCQMediumJEE 2024
  32. 32Let A₁, A₂, A₃ be the three A.P. with the same common difference d and having their first terms as A, A+1, A+2, respectively. Let a, b, c…NVAMediumJEE 2023
  33. 33Let a, b, c > 1, a³, b³ and c³ be in A.P., and log_b a, logₐ c and log_c b be in G.P. If the sum of the first 20 terms of an A.P., whose…MCQMediumJEE 2023
  34. 34The 8th common term of the series S₁ = 3 + 7 + 11 + 15 + 19 + …, S₂ = 1 + 6 + 11 + 16 + 21 + …, isNVAMediumJEE 2023
  35. 35Let a₁, a₂, …, aₙ be in A.P. If a₅ = 2a₇ and a₁₁ = 18, then 12 ( 1/(√a₁₀ + √a₁₁) + 1/(√a₁₁ + √a₁₂) + … + 1/(√a₁₇ + √a₁₈)) is equal to:NVAMediumJEE 2023
  36. 36Let a₁, a₂, a₃, … be an A.P. If a₇ = 3, the product a₁ a₄ is minimum and the sum of its first n terms is zero, then n! - 4a_n(n+2) is equal…MCQMediumJEE 2023
  37. 37Let a₁ = 8, a₂, a₃, … aₙ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170, then the product of…NVAMediumJEE 2023
  38. 38The sum of the common terms of the following three arithmetic progressions: - 3, 7, 11, 15, …, 399, - 2, 5, 8, 11, …, 359, - 2, 7, 12, 17,…NVAMediumJEE 2023
  39. 39Let a₁, a₂, a₃,..., aₙ be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then lim_n→∞…MCQMediumJEE 2023
  40. 40The sum of all terms of the arithmetic progression 3, 8, 13,..., 373, which are not divisible by 3, is:NVAEasyJEE 2023
  41. 41Let s₁, s₂, s₃, …, s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1, 2, 3, …, 10 and the common differences are…MCQMediumJEE 2023

Frequently asked questions

Our bank has 41 previous-year JEE Mathematics questions tagged to Arithmetic Progression (AP), drawn from JEE papers between 2023 and 2026, including 7 from 2026 alone. Each comes with a full step-by-step solution.

Arithmetic Progression (AP) is rated Basic overall for JEE Mathematics. The PYQs on this page break down as 38 medium, 3 easy.

Of the 41 previous-year questions on Arithmetic Progression (AP), 31 are multiple-choice (MCQ) and 10 are numerical-value (NVA) questions.

Based on recent paper analysis, Arithmetic Progression (AP) is worth about 3 marks in JEE Main. It sits in Sequences & Series, a Class 11 Mathematics chapter.

More Sequences & Series topics

Sum of Series53Geometric Progression (GP)22AM-GM Relationship0Harmonic Progression (HP)0

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