Enter the explicit rule for the geometric sequence. 1/4, 1/2, 1, 2, 4, …

Question

Enter the explicit rule for the geometric sequence.

1/4, 1/2, 1, 2, 4, …

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Helga 3 years 2021-08-22T13:29:24+00:00 1 Answers 4 views 0

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    2021-08-22T13:30:29+00:00

    Answer:

    a_n = (\frac{1}{4})2^{n-1}

    Step-by-step explanation:

    Geometric sequence:

    In a geometric sequence, the quotient between consecutive terms is the same, and this quotient is given by q.

    The explicit rule of a geometric sequence is given by:

    a_n = a_1q^{n-1}

    In which a_1 is the first term.

    1/4, 1/2, 1, 2, 4

    This means that a_1 = \frac{1}{4}, and:

    q = \frac{4}{2} = \frac{2}{1} = \frac{1}{\frac{1}{2}} = \frac{\frac{1}{2}}{\frac{1}{4}} = 2

    So the explicit rule is:

    a_n = (\frac{1}{4})2^{n-1}

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