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14 July, 00:24

Identify and extend the pattern to find the next number in this sequence: 2, 8, 32, 128, ... A. 152 B. 134 C. 224 D. 512

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  1. 14 July, 02:47
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    Given that the sequence is:

    2, 8, 32, 128, ...

    The series is a geometric sequence because there is a common ratio between the consecutive numbers. Thus it will follow the explicit form given by:

    an=ar^ (n-1)

    where:

    a=first term

    r = common ratio

    n = nth term

    from the sequence:

    a=2

    r=8/2=4

    thus the explicit formula for the sequence is:

    an=2 (4^ (n-1))

    thus the next term which is the fifth term will be:

    a5=2 (4^ (5-1))

    a5=512

    Answer: D
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