Sequences & Series JEE Main PYQs PDF, 2020–2026

Sequences & Series questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 246 of the 247 asked.

Topic-wise weightage by year

How many Sequences & Series questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 33 JEE Main 2026 Sequences & Series questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Arithmetic Progression

   Let $\alpha=3+4+8+9+13+14+\ldots$ upto 40 terms. If $(\tan \beta)^{{\frac{\alpha}{1020}}}$ is a root of the equation $x^{2}+x-2=0,\beta\in \left(0,\frac{\pi}{2}\right)$, then $\sin^{2}\beta+3\cos^{2}\beta$ is equal to :

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2. JEE Main 2026 · 6 Apr · Shift 1 · Telescoping Series

   The value of $1^{3}-2^{3}+3^{3}-\ldots +{15}^{3}$ is:

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3. JEE Main 2026 · 6 Apr · Shift 1 · Arithmetic Progression

   The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8 . If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

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4. JEE Main 2026 · 6 Apr · Shift 1 · Arithmetic Progression

   For the functions $f(\theta)=\alpha\tan^{2}\theta+\beta\cot^{2}\theta$, and $g(\theta)=\alpha\sin^{2}\theta+\beta\cos^{2}\theta,\alpha>\beta>0$, let $\underset{{0<\theta<\frac{\pi}{2}}}{min}f(\theta)=\underset{{0<\theta<\pi}}{max}g(\theta)$. If the first term of a G.P. is $\left(\frac{\alpha}{2\beta}\right)$, its common ratio is $\left(\frac{2\beta}{\alpha}\right)$ and the sum of its first 10 terms is $\frac{m}{n},\gcd (m,n)=1$, then $m+n$ is equal to $\_\_\_\_$ .

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5. JEE Main 2026 · 6 Apr · Shift 2 · Telescoping Series

   The sum $1+\frac{1}{2}\left(1^{2}+2^{2}\right)+\frac{1}{3}\left(1^{2}+2^{2}+3^{2}\right)+\ldots$ upto 10 terms is equal to :

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6. JEE Main 2026 · 6 Apr · Shift 2 · Arithmetic Progression

   Consider the quadratic equation $\left(n^{2}-2n+2\right)x^{2}-3x+\left(n^{2}-2n+2\right)^{2}=0,n\in {\mathbf{R}}$. Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is $\alpha$ and the common ratio is $\frac{\alpha}{\beta}$, is :

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7. JEE Main 2026 · 5 Apr · Shift 1 · Arithmetic Progression

   Let the sum of the first $n$ terms of an A.P. be $3n^{2}+5n$. Then the sum of squares of the first 10 terms of the A.P. is:

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8. JEE Main 2026 · 5 Apr · Shift 2 · Arithmetic Progression

   Let ${\mathrm{A}}_{1},{\ \mathrm{A}}_{2},{\ \mathrm{A}}_{3},\ldots \ldots..,{\mathrm{A}}_{{39}}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of ${\mathrm{A}}_{{25}},{\ \mathrm{A}}_{{28}},{\ \mathrm{A}}_{{31}}$ and ${\mathrm{A}}_{{36}}$ is equal to :

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9. JEE Main 2026 · 5 Apr · Shift 1 · Telescoping Series

   $\sum_{{n=1}}^{{10}}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:

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10. JEE Main 2026 · 5 Apr · Shift 2 · Telescoping Series

    If the sum of the first 10 terms of the series $\frac{1}{1+1^{4}\times 4}+\frac{2}{1+2^{4}\times 4}+\frac{3}{1+3^{4}\times 4}+\frac{4}{1+4^{4}\times 4}+\ldots \ldots$. is $\frac{m}{n},\gcd (m,n)=1$, then $m+n$ is equal to :

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11. JEE Main 2026 · 4 Apr · Shift 1 · Arithmetic Progression

    The first term of an A.P. of 30 non-negative terms is $\frac{10}{3}$. If the sum of this A.P. is the cube of its last term, then its common difference is:

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12. JEE Main 2026 · 4 Apr · Shift 2 · Geometric Progression

    Let $\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots\infty$ and $\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots\infty$. Then the value of $(0.2)^{\log_{\sqrt{5}}(\alpha)}+(0.04)^{\log_{5}(\beta)}$ is equal to:

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Sample questions from recent papers

The free PDF above has all 246 questions grouped by topic, with an answer key.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020