Sequences and Series

  1. Find out the next term in the series 7, 11, 13, 17, 19, ...
    1. 21
    2. 23
    3. 27
    4. None of these
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    Given series is a consecutive prime number series.

    Correct Option: B

    Given series is a consecutive prime number series. Therefore, the next term will be 23.

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  1. Find the missing term 6, ?, 21, 33, 48
    1. 14
    2. 20
    3. 12
    4. 18
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    Series Pattern
    +6, +9, +12, +15...

    Correct Option: C

    Series Pattern
    +6, +9, +12, +15....
    ∴ Missing term = 6 + 6 = 12

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  1. Find the value of the expression 1 - 2 + 3 - 4 + 5 - 6 + 7 + .... upto 100 terms . ?
    1. -150
    2. -60
    3. -100
    4. -50
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    (1 - 2) = -1
    (3 - 4) = -1
    (5 - 6) = -1

    Correct Option: D

    (1 - 2) = -1
    (3 - 4) = -1
    (5 - 6) = -1
    and so on.
    ∴ Total terms of -1 will be 50.
    ∴ Answer = -1 x 50 = -50

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  1. If A represents the arithmetic mean, H represents the harmonic mean and G represents the geometric mean, then what is the relation between them ?
    1. A x H = G
    2. A x H = G2
    3. A/H = G2
    4. A/H = G
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    A = (a + b)/2,
    1/H = (1/a + 1/b)/2
    ⇒ H = 2ab/(a +b),
    G = √ab

    Correct Option: B

    A = (a + b)/2,
    1/H = (1/a + 1/b)/2
    ⇒ H = 2ab/(a +b),
    G = √ab
    ∴ A x H = {(a + b)/2} x {2ab/(a + b)} = ab = G2
    ∴ A x H = G2

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  1. 4, 12, 36, ?, 324, 972
    1. 108
    2. 125
    3. 215
    4. 312
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    Series pattern
    Every next element = 3 x previous element

    Correct Option: A

    Series pattern
    Every next element = 3 x previous element
    ∴ Missing term = 3 x 36 = 108

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