Sequences and Series


  1. Find out the wrong number in the series.
    190, 166, 145, 128, 112, 100, 91









  1. View Hint View Answer Discuss in Forum

    The pattern is :
    190 – 24 = 166
    166 – 21 = 145
    145 – 18 = 127 ≠ 128
    ........... and so on.

    Correct Option: D

    The pattern is :
    190 – 24 = 166
    166 – 21 = 145
    145 – 18 = 127 ≠ 128
    Since , 128 is wrong term . so , 127 is correct term .
    127 – 15 = 112
    112 – 12 = 100
    100 – 9 = 91
    Thus , wrong number in the series is 128.


  1. Find out the wrong number in the sequence : 40960, 10240, 2560, 640, 200, 40, 10









  1. View Hint View Answer Discuss in Forum

    The pattern is :
    40960 ÷ 4 = 10240
    10240 ÷ 4 = 2560
    2560 ÷ 4 = 640
    640 ÷ 4 = 160 ≠ 200

    Correct Option: B

    The pattern is :
    40960 ÷ 4 = 10240
    10240 ÷ 4 = 2560
    2560 ÷ 4 = 640
    640 ÷ 4 = 160 ≠ 200
    Since , 200 is wrong number . so , 160 is correct number .
    160 ÷ 4 = 40
    40 ÷ 4 = 10
    Thus , required answer is 200.



  1. The next number of the sequence 3, 5, 9, 17, 33, .... is









  1. View Hint View Answer Discuss in Forum

    The pattern is :
    3 + 2 = 5
    5 + 2 × 2 = 5 + 4 = 9
    9 + 2 × 4 = 9 + 8 = 17
    17 + 2 × 8 = 17 + 16 = 33
    33 + 2 × 16 = 33 + 32 = ?

    Correct Option: A

    The pattern is :
    3 + 2 = 5
    5 + 2 × 2 = 5 + 4 = 9
    9 + 2 × 4 = 9 + 8 = 17
    17 + 2 × 8 = 17 + 16 = 33
    33 + 2 × 16 = 33 + 32 = ?
    ∴ ? = 65
    Thus , The next number of the sequence is 65 .


  1. The next number of the sequence
    1
    ,
    3
    ,
    5
    ,
    7
    ,.....is
    24816









  1. View Hint View Answer Discuss in Forum

    Sequence of numerators :
    ⇒ 1, 3, 5, 7, 9 which is odd numbers .
    Sequence of denominators :
    ⇒ 2, 4, 8, 16, 32 which is represents 21 , 22 , 23 , 24 , 25 numbers .

    Correct Option: D

    Sequence of numerators :
    ⇒ 1, 3, 5, 7, 9 which is odd numbers .
    Sequence of denominators :
    ⇒ 2, 4, 8, 16, 32 which is represents 21 , 22 , 23 , 24 , 25 numbers .

    ∴ Next fraction =
    9
    32



  1. When simplified, the sum
    1
    +
    1
    +
    1
    +
    1
    +
    1
    +......+
    1
    is equal to
    26122030n(n+1)









  1. View Hint View Answer Discuss in Forum

    Expression =
    1
    +
    1
    +
    1
    +
    1
    + .......... +
    1
    261220n(n + 1)

    =
    1
    +
    1
    +
    1
    +
    1
    + .......... +
    1
    1 × 22 × 33 × 44 × 5n(n + 1)

    = 1 -
    1
    +
    1
    -
    1
    +
    1
    -
    1
    +
    1
    -
    1
    ......... +
    1
    -
    1
    2233445nn + 1

    Correct Option: D

    Expression =
    1
    +
    1
    +
    1
    +
    1
    + .......... +
    1
    261220n(n + 1)

    =
    1
    +
    1
    +
    1
    +
    1
    + .......... +
    1
    1 × 22 × 33 × 44 × 5n(n + 1)

    = 1 -
    1
    +
    1
    -
    1
    +
    1
    -
    1
    +
    1
    -
    1
    ......... +
    1
    -
    1
    2233445nn + 1

    Expression = 1 -
    1
    =
    n + 1 - 1
    =
    n
    n + 1n + 1n + 1