PrepWiser › Learn › Mathematics › Sequences & SeriesSequences & Series — JEE Main PYQs & Practice Questions Sequences & Series is a Mathematics chapter in the JEE Main syllabus. This page brings together 262 previous-year and practice questions on Sequences & Series, organised into 6 topics: Arithmetic Progression, Geometric Progression, Harmonic Progression, Arithmetico-Geometric Progression, Special Sums and Telescoping Series. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Arithmetic Progression Let a₁, a₂, a₃, ..... be an A.P. If (a₁ + a₂ + .... + a₁₀)/(a₁ + a₂ + .... + aₚ) =… Let α and β be two real numbers such that α + β = 1 and αβ = -1. Let pₙ = (α)ⁿ + (β)ⁿ… If 3^(2 sin 2α - 1), 14 and 3^(4 - 2 sin 2α) are the first three terms of an A.P. for… Let 2ⁿᵈ, 8ᵗʰ and 44ᵗʰ terms of a non-constant A. P. be respectively the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ… In an A.P., the sixth term a₆=2. If the product a₁ a₄ a₅ is the greatest, then the… Let α=3+4+8+9+13+14+… upto 40 terms. If (tan β)^(α/1020) is a root of the equation… For three positive integers p, q, r, x^(pq²) = y^(qr) = z^(p²r) and r = pq + 1 such that… Let A₁,A₂,A₃ be the three A.P. with the same common difference d and having their first… Let a₁, a₂, a₃, … be in an A.P. such that Σk=1¹² a₂ₖ₋₁=-72/5 a₁, a₁ ≠ 0. If Σk=1ⁿ aₖ=0… The interior angles of a polygon with n sides, are in an A.P. with common difference 6°… If log ₃2,log ₃(2ˣ - 5),log ₃( 2ˣ - 7/2 ) are in an arithmetic progression, then the… The common difference of the A.P.: a₁,a₂,…,aₘ is 13 more than the common difference of… Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common… Three numbers in AP have sum 15 and product 80. If they are a-d, a, a+d, then a = x. If the 10ᵗʰ term of an A.P. is 1/20 and its 20ᵗʰ term is 1/10, then the sum of its first… The 20ᵗʰ term from the end of the progression 20,19 1/4, 18 1/2, 17 3/4, …,-129 1/4 is : Let Tᵣ be the rᵗʰ term of an A.P. If for some m, Tₘ=1/25, T₂₅=1/20, and 20 Σᵣ₌₁²⁵ Tᵣ=13… The 8ᵗʰ common term of the series S₁=3+7+11+15+19+… . . ; ; S₂=1+6+11+16+21+… . . is : Let Sₙ denote the sum of the first n terms of an arithmetic progression. If S₁₀=390 and… The common difference of the A.P. b₁, b₂, … , bₘ is 2 more than the common difference of… Geometric Progression Consider two G.Ps. 2, 2², 2³, ..... and 4, 4², 4³, .... of 60 and n terms respectively… For the two positive numbers a,b, if a,b and 1/18 are in a geometric progression, while… If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the… Let a₁, a₂, a₃, … be a G.P. of increasing positive terms. If a₁ a₅=28 and a₂+a₄=29, then… Let { aₖ} and { bₖ} ,k ∈ N, be two G.P.s with common ratios r₁ and r₂ respectively such… Let a₁,a₂,a₃,… be an A.P. and g₁=a₁,g₂,g₃,… be an increasing G.P. If a₁=a₂+g₂=1 and… The minimum value of f(x) = a^(aˣ) + a^(1 - aˣ), where a, x ∈ R and a > 0, is equal to : Let x₁, x₂, x₃, …, x₂₀ be in geometric progression with x₁=3 and the common ratio 1/2. A… The remainder on dividing 1 + 3 + 3² + 3³ + ..... + 3²⁰²¹ by 50 is _________. Let a and b be be two distinct positive real numbers. Let 11ᵗʰ term of a GP, whose first… Let A₁, A₂, A₃, ....... be an increasing geometric progression of positive real numbers… If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296… Let x₁, x₂, x₃, x₄ be in a geometric progression. If 2,7,9,5 are subtracted respectively… Let a₁,a₂,a₃,... be a GP of increasing positive numbers. If the product of fourth and… The sum of the first three terms of a G.P. is S and their product is 27. Then all such S… In an increasing geometric series, the sum of the second and the sixth term is 25/2 and… The sum of first four terms of a geometric progression (G. P.) is 65/12 and the sum of… For 0 < c < b < a, let (a+b-2 c) x²+(b+c-2 a) x+(c+a-2 b)=0 and α ≠ 1 be one of its… Let a₁ , a₂ , a₃ ,....... be a G.P. such that a₁ < 0, a₁ + a₂ = 4 and a₃ + a₄ = 16. If… Let A₁, A₂, A₃, ....... be squares such that for each n ≥ 1, the length of the side of… Harmonic Progression If a, b, c are in HP, then: The harmonic mean of 2 and 4 is x. Let 0 < z < y < x be three real numbers such that 1/x, 1/y, 1/z are in an arithmetic… If a, b, c are in HP, then a, b, c are also in GP. Arithmetico-Geometric Progression The sum of the infinite series 1 + 5/6 + 12/6² + 22/6³ + 35/6⁴ + 51/6⁵ + 70/6⁶ +… The sum 1 + 2 . 3 + 3 . 3² + ......... + 10 . 3⁹ is equal to : Let S = 2 + 6/7 + 12/7² + 20/7³ + 30/7⁴ + ...... Then 4S is equal to The sum of the infinite series 1 + 2/3 + 7/3² + 12/3³ + 17/3⁴ + 22/3⁵ + ...... is equal… If 7=5+1/7(5+α)+1/7²(5+2 α)+1/7³(5+3 α)+… … … … ∞, then the value of α is : Let S be the sum of the first 9 terms of the series : x + ka + x² + (k + 2)a + x³ + (k +… Let for f(x) = a₀x² + a₁x + a₂, f'(0) = 1 and f'(1) = 0. If a₀, a₁, a₂ are in an… Let the first term of a series be T₁=6 and its rᵗʰ term Tᵣ=3 Tᵣ₋₁+6ʳ, r=2,3… Suppose a₁, a₂, 2, a₃, a₄ be in an arithmetico-geometric progression. If the common… Let f(x)=Σk=1¹⁰ k xᵏ, x ∈ ℝ. If 2 f(2)+f′(2)=119(2)ⁿ+1 then n is equal to ___________ Three numbers are in an increasing geometric progression with common ratio r. If the… If S(x)=(1+x)+2(1+x)²+3(1+x)³+…+60(1+x)⁶⁰, x ≠ 0, and (60)² S(60)=a(b)ᵇ+b, where a, b ∈… 6/3²⁶+(10· 1)/3²⁵+(10· 2)/3²⁴+(10· 2²)/3²³+… +(10· 2²⁴)/3 is equal to : Let { aₙ} ₙ₌₀^∞ be a sequence such that a₀ = a₁ = 0 and aₙ₊₂ = 2aₙ₊₁ - aₙ + 1 for all n… Let a₁=b₁=1 and aₙ = aₙ₋₁ + (n - 1),bₙ = bₙ₋₁ + aₙ₋₁,∀ n ≥ 2. If S = Σₙ₌₁¹⁰ bₙ/2ⁿ and T… Special Sums If 8=3+1/4(3+p)+1/4²(3+2 p)+1/4³(3+3 p)+… … ∞, then the value of p is ____________. If 0 < x < 1 and y = 1/2x² + 2/3x³ + 3/4x⁴ + ...., then the value of e 1 + y at x = 1/2… Let α, β be roots of x²+√2 x-8=0. If Uₙ=αⁿ+βⁿ, then (U₁₀+√2 U₉)/(2 U₈) is equal to… Let α and β be the roots of the equation 5x² + 6x – 2 = 0. If Sₙ = αⁿ + βⁿ, n = 1, 2… If S = 7/5 + 9/5² + 13/5³ + 19/5⁴ + ...., then 160 S is equal to ________. The value of (2.¹P₀ – 3.²P₁ + 4.³P₂ .... up to 51ᵗʰ term) + (1! – 2! + 3! – ..... up to… Let α and β be the roots of the equation x² - x - 1 = 0. If pₖ = ( α )ᵏ + ( β )ᵏ , k ≥… The product 2^(1/4).4^(1/16).8^(1/48).16^(1/128) ... to ∞ is equal to : Let the positive integers be written in the form : 1; 2, 3; 4, 5, 6; 7, 8, 9, 10; ..., ⋱… If 1+(1–2².1)+(1–4².3)+(1-6².5)+......+(1-20².19)= α - 220β, then an ordered pair ( α ,β… Let { aₙ }ₙ₌₁^∞ be a sequence such that a₁ = 1, a₂ = 1 and aₙ₊₂ = 2aₙ₊₁ + aₙ for all n ≥… The sum Σₖ₌₁²⁰ ( 1 + 2 + 3 + ... + k ) is : If the sum of the first ten terms of the series 1/5 + 2/65 + 3/325 + 4/1025 + 5/2501 +… Sₙ(x) = log a 1/2 x + log a 1/3 x + log a 1/6 x + log a 1/11 x + log a 1/18 x + log a… If 1+(√3-√2)/(2 √3)+(5-2 √6)/18+(9 √3-11 √2)/(36 √3)+(49-20 √6)/180+… upto… The series of positive multiples of 3 is divided into sets… If A = Σₙ₌₁^∞ 1/( 3 + ( - 1)ⁿ )ⁿ and B = Σₙ₌₁^∞ ( - 1)ⁿ/( 3 + ( - 1)ⁿ )ⁿ , then A/B is… Let Sₙ = 1 . (n - 1) + 2 . (n - 2) + 3 . (n - 3) + ..... + (n - 1) . 1, n ≥ 4. The sum… The value of (1 × 2²+2 × 3²+…+100 ×(101)²)/(1² × 2+2² × 3+… .+100² × 101) is Let α=1²+4²+8²+13²+19²+26²+… upto 10 terms and β=Σn=1¹⁰ n⁴. If 4 α-β=55 k+40, then k is… Telescoping Series More Mathematics chapters Frequently asked questions How many Sequences & Series questions are there for JEE Main? PrepWiser has 262 Sequences & Series questions for JEE Main, grouped into 6 topics such as Arithmetic Progression, Geometric Progression and Harmonic Progression.
Are these Sequences & Series questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Sequences & Series questions? Open any Sequences & Series question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.