JEE Advanced Sequences and Series — previous year questions
22 questions from 2026, 2025, 2023, 2022, 2020, 2019, 2018, 2016, 2015, 2013, 2012, 2011, 2010, 2009, 2008.
- Let a, b, c be positive integers in arithmetic progression such that the equation ax² + bx + c = 0 has only…
- Let R denote the set of all real numbers. Let f : R → R be a function such that f(x) > 0 for all x ∈ R, and…
- Let 7̅5̅⋯̅5̅7̅ denote the (r+2) digit number where the first and the last digits are 7 and the remaining r…
- Let l₁, l₂, …, l₁₀₀ be consecutive terms of an arithmetic progression with common difference d₁, and let w₁,…
- Let a₁, a₂, a₃, … be an arithmetic progression with a₁ = 7 and common difference 8. Let T₁, T₂, T₃, … be such…
- Let a₁, a₂, a₃, … be a sequence of positive integers in arithmetic progression with common difference 2.…
- Let m be the minimum possible value of log₃(3^(y₁) + 3^(y₂) + 3^(y₃)), where y₁, y₂, y₃ are real numbers for…
- Let AP(a;d) denote the set of all the terms of an infinite arithmetic progression with first term a and…
- Let α and β be the roots of x² - x - 1 = 0, with α > β. For all positive integers n, define aₙ = (αⁿ - βⁿ)/(α…
- Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, …, and Y be the…
- The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is…
- Let bᵢ > 1 for i = 1, 2, …, 101. Suppose logₑ b₁, logₑ b₂, …, logₑ b₁₀₁ are in Arithmetic Progression (A.P.)…
- Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum…
- A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and…
- Let Sₙ = ∑ₖ₌₁⁴ⁿ (-1)^((k(k+1))/2) k². Then Sₙ can take value(s)
- Let a₁, a₂, a₃, … be in harmonic progression with a₁ = 5 and a₂₀ = 25. The least positive integer n for which…
- Let a₁, a₂, a₃, …, a₁₀₀ be an arithmetic progression with a₁ = 3 and Sₚ = ∑ᵢ₌₁ᵖ aᵢ, 1 ≤ p ≤ 100. For any…
- Let Sₖ, k = 1, 2, ....., 100, denote the sum of the infinite geometric series whose first term is (k-1)/k!…
- Let a₁, a₂, a₃, …, a₁₁ be real numbers satisfying a₁ = 15, 27 - 2a₂ > 0 and aₖ = 2aₖ₋₁ - aₖ₋₂ for k = 3, 4,…
- In the sum of first n terms of an A.P. is cn², then the sum of squares of these n terms is
- A straight line through the centroid G of a triangle PQR intersects the side QR at the point S and the…
- Suppose four distinct positive numbers a₁, a₂, a₃, a₄ are in G.P. Let b₁ = a₁, b₂ = b₁ + a₂, b₃ = b₂ + a₃ and…