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Sequence and Series

CDS Maths. Try each one first, then open its answer.

Top 10 CDS 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 3 times: CDS 1 2018, CDS 2 2020, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    28
    The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers ?

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  2. Question 2

    This type asked 3 times: CDS 2 2016, CDS 1 2021, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    35
    What is 312×22+522×32+732×42+…\frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \ldots equal to ?

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  3. Question 3

    This type asked 3 times: CDS 2 2018, CDS 1 2020, CDS 2 2022. This one: CDS 2 2022 See all 3 of this type

    61
    If xx is the harmonic mean between yy and zz, then which one of the following is correct ?

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  4. Question 4

    This type asked 2 times: CDS 1 2024, CDS 2 2024. This one: CDS 2 2024 See all 2 of this type

    22
    What is the geometric mean of 3, 9, 27, 81, 243, 729, 2187 ?

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  5. Question 5

    Asked once: CDS 2 2020 (same type asked 3 times) See all 3 of this type

    100
    The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic mean ?

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  6. Question 6

    Asked once: CDS 1 2021 (same type asked 3 times) See all 3 of this type

    30
    If 11×2+12×3+13×4+⋯+1n(n+1)=99100\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \cdots + \frac{1}{n(n + 1)} = \frac{99}{100} then what is the value of nn ?

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  7. Question 7

    Asked once: CDS 1 2020 (same type asked 3 times) See all 3 of this type

    45
    For two observations, the sum is SS and product is PP. What is the harmonic mean of these two observations?

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  8. Question 8

    Asked once: CDS 1 2024 (same type asked 2 times) See all 2 of this type

    42
    Let the positive numbers a1,a2,a3,…,a3na_1, a_2, a_3, \ldots, a_{3n} be in GP. If P is the GM of a1,a2,a3,…,ana_1, a_2, a_3, \ldots, a_n and Q is the GM of an+1,an+2,an+3,…,a3na_{n+1}, a_{n+2}, a_{n+3}, \ldots, a_{3n}, then what is the GM of 3n numbers ?

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  9. Question 9

    Asked once: CDS 1 2018 (same type asked 3 times) See all 3 of this type

    52
    The arithmetic mean of two numbers is 10 and their geometric mean is 8. What are the two numbers?

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  10. Question 10

    Asked once: CDS 2 2016 (same type asked 3 times) See all 3 of this type

    25
    What is 1+112+122+1+122+132+…+1+120072+120082\sqrt{1 + \frac{1}{1^2} + \frac{1}{2^2}} + \sqrt{1 + \frac{1}{2^2} + \frac{1}{3^2}} + \ldots + \sqrt{1 + \frac{1}{2007^2} + \frac{1}{2008^2}} equal to ?

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