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30 December, 05:30

4, 12, 16, 48, 64, 192,

next number in the series?

i tried 4 x 3, + 4, x 3, + 4 but stopped working at 48.

+3
Answers (1)
  1. 30 December, 05:32
    0
    The next term in the series is 256

    Step-by-step explanation:

    Lets explain how to solve the problem

    The series is:

    4, 12, 16, 48, 64, 192

    If we subtract 12 - 4 = 8

    If we subtract 16 - 12 = 4

    The difference is not constant then it's not an arithmetic series

    If we divide 12 by 4 the answer is 3

    If we divide 16 by 12 the answer is 4/3

    The ratio is not constant then it's not a geometric series

    So lets look to the odd positions 1st, 3rd, 5th, they are:

    4, 16, 64

    16 : 4 = 4

    64 : 16 = 4

    There is a constant ratio 4 between each 2 consecutive odd position

    terms

    Lets look to the even positions 2nd, 4th, 6th, they are:

    12, 48, 192

    48 : 12 = 4

    192 : 48 = 4

    There is a constant ratio 4 between each 2 consecutive even position

    terms

    Now we can find any term is the series by multiply the previous odd

    position by 4 if the term in odd position and multiply the previous

    even position by 4 if the term in even position

    The next term is in the 7th position, then the next term is:

    The number in the 5th position * 4

    ∵ The number in the 5th position is 64

    ∴ The number in the 7th position = 64 * 4 = 256

    * The next term in the series is 256
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