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Sequences and Series

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 10 times: 2021 Paper 25, 26 Jun 2022, 28 Jun 2022, 29 Jan 2023, 13 Apr 2023, 8 Apr 2024, 22 Jan 2025, 3 Apr 2025, 7 Apr 2025, 21 Jan 2026 S1. This one: 21 Jan 2026 S1 See all 10 of this type

    56
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots. be a G.P. of increasing positive terms such that a2⋅a3⋅a4=64a_{2}\cdot a_{3}\cdot a_{4}= 64 and a1+a3+a5=8137a_{1}+a_{3}+a_{5}=\frac{813}{7}. Then a3+a5+a7a_{3}+a_{5}+a_{7} is equal to :

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  2. Question 2

    This type asked 9 times: 2021 Paper 10, 2021 Paper 13, 2021 Paper 14, 2021 Paper 23, 30 Jan 2024, 1 Feb 2024, 23 Jan 2025, 24 Jan 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 9 of this type

    70
    If 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 is

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  3. Question 3

    This type asked 9 times: 2021 Paper 14, 2021 Paper 25, 25 Jun 2022, 29 Jul 2022, 6 Apr 2023, 10 Apr 2023, 11 Apr 2023, 27 Jan 2024, 24 Jan 2025. This one: 24 Jan 2025 See all 9 of this type

    135
    If 7=5+17(5+α)+172(5+2α)+173(5+3α)+⋯7 = 5 + \frac{1}{7}(5+\alpha) + \frac{1}{7^{2}}(5+2\alpha) + \frac{1}{7^{3}}(5+3\alpha) + \cdots upto ∞\infty, then the value of α\alpha is:

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  4. Question 4

    This type asked 8 times: 27 Jun 2022, 26 Jul 2022, 1 Feb 2023, 31 Jan 2024, 2 Apr 2025, 4 Apr 2025, 28 Jan 2026 S2, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 8 of this type

    55
    If the sum of the first 10 terms of the series 11+14×4+21+24×4+31+34×4+41+44×4+…\frac{1}{1 +1^{4}\times 4}+\frac{2}{1 +2^{4}\times 4}+\frac{3}{1 +3^{4}\times 4}+\frac{4}{1 +4^{4}\times 4}+ \ldots is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to :

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  5. Question 5

    This type asked 8 times: 2021 Paper 9, 2021 Paper 24, 25 Jul 2022, 29 Jul 2022, 30 Jan 2023, 9 Apr 2024, 24 Jan 2025, 28 Jan 2025. This one: 28 Jan 2025 See all 8 of this type

    138
    For positive integers nn, if 4an=(n2+5n+6)4a_{n}=\left( n^{2}+ 5n + 6 \right) and Sn=∑k=1n(1ak)S_{n}=\sum_{k = 1}^{n} \left( \frac{1}{a_{k}} \right), then the value of 507 S2025507{\text{ }S}_{2025} is :

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  6. Question 6

    This type asked 7 times: 29 Jun 2022, 30 Jan 2023, 1 Feb 2023, 27 Jan 2024, 1 Feb 2024, 4 Apr 2025, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 7 of this type

    55
    Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 6. Then the number of elements in A∩BA\cap B, which are divisible by 3 , is :

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  7. Question 7

    This type asked 6 times: 2021 Paper 24, 2021 Paper 26, 30 Jan 2023, 1 Feb 2023, 3 Apr 2025, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 6 of this type

    52
    The value of ∑k=1∞(−1)k+1(k(k+1)k!)\sum_{k= 1}^{\infty} ( - 1)^{k+ 1}\left( \frac{k(k+ 1)}{k!} \right) is :

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  8. Question 8

    This type asked 5 times: 31 Jan 2023, 6 Apr 2023, 13 Apr 2023, 4 Apr 2025, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    55
    The value of 13−23+33−….+1531^{3}-2^{3}+3^{3}- \ldots. +15^{3} is:

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  9. Question 9

    This type asked 5 times: 2021 Paper 22, 1 Feb 2024, 4 Apr 2024, 7 Apr 2025, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 5 of this type

    74
    Suppose a,b,ca,b,c are in A.P. and a2,2 b2,c2a^{2},2{\text{ }b}^{2},c^{2} are in G.P. If a<b<ca < b < c and a+b+c=1a + b + c = 1, then 9(a2+b2+c2)9\left( a^{2} + b^{2} + c^{2} \right) is equal to ____\_\_\_\_.

  10. Question 10

    This type asked 5 times: 6 Apr 2023, 8 Apr 2023, 10 Apr 2023, 30 Jan 2024, 3 Apr 2025. This one: 3 Apr 2025 See all 5 of this type

    57
    The sum 1+3+11+25+45+71+…1 + 3 + 11 + 25 + 45 + 71 + \ldots upto 20 terms, is equal to

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