Sequences and Series

JEE Advanced · Mathematics · 25 past questions

1. Q1 2023 Paper 1

   Let $7\overbrace{5\cdots5}^{r}7$ denote the $(r+2)$ digit number where the first and the last digits are 7…

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2. Q2 2022 Paper 1

   Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1 = 7$ and common difference $8$. Let…

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3. Q3 2020 Paper 1

   Let $a_1, a_2, a_3, \ldots$ be a sequence of positive integers in arithmetic progression with common…

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4. Q4 2019 Paper 1

   Let $\alpha$ and $\beta$ be the roots of $x^2-x-1=0$, with $\alpha>\beta$. For all positive integers $n$…

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5. Q5 2019 Paper 1

   Let $AP(a;d)$ denote the set of all the terms of an infinite arithmetic progression with first term $a$ and…

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6. Q6 2018 Paper 1

   Let $X$ be the set consisting of the first 2018 terms of the arithmetic progression $1, 6, 11, \dots$, and…

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7. Q7 2017 Paper 1

   The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is…

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8. Q8 2016 Paper 2

   Let $b_i>1$ for $i=1,2,\ldots,101$. Suppose $\log_e b_1,\log_e b_2,\ldots,\log_e b_{101}$ are in Arithmetic…

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9. Q9 2015 Paper 2

   Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum…

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10. Q10 2014 Paper 1

    Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric…

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11. Q11 2013 Paper 1

    Let $S_n=\sum_{k=1}^{4n}(-1)^{\frac{k(k+1)}{2}}k^2$. Then $S_n$ can take value(s)

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12. Q12 2013 Paper 1

    A pack contains $n$ cards numbered from 1 to $n$. Two consecutive numbered cards are removed from the pack…

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13. Q13 2012 Paper 2

    Let $a_1, a_2, a_3, \ldots$ be in harmonic progression with $a_1 = 5$ and $a_{20} = 25$. The least positive…

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14. Q14 2011 Paper 1

    Let $a_1, a_2, a_3, \ldots, a_{100}$ be an arithmetic progression with $a_1 = 3$ and…

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15. Q15 2011 Paper 1

    The minimum value of the sum of real numbers $a^{-5}, a^{-4}, 3a^{-3}, 1, a^8$ and $a^{10}$ with $a > 0$ is

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16. Q16 2010 Paper 1

    Let $S_k$, $k = 1, 2, \ldots, 100$, denote the sum of the infinite geometric series whose first term is…

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17. Q17 2010 Paper 2

    Let $a_1, a_2, a_3, \ldots, a_{11}$ be real numbers satisfying…

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18. Q18 2009 Paper 2

    If the sum of first $n$ terms of an A.P. is $cn^2$, then the sum of squares of these $n$ terms is

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19. Q19 2008 Paper 2

    Suppose four distinct positive numbers $a_1, a_2, a_3, a_4$ are in G.P. Let $b_1=a_1$, $b_2=b_1+a_2$…

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20. Q20 2007 Paper 1

    Paragraph for Question Nos. 58 to 60…

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21. Q21 2007 Paper 1

    M58-60: Paragraph for Question Nos. 58 to 60…

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22. Q22 2007 Paper 1

    M58-60: Paragraph for Question Nos. 58 to 60…

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23. Q23 2007 Paper 2

    Which one of the following statements is correct?

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24. Q24 2007 Paper 2

    Which one of the following statements is correct?

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25. Q25 2007 Paper 2

    Which one of the following statements is correct?

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