Find the indicated term of the given geometric sequence. a1 = 14, r = –2, n = 11

Question

Find the indicated term of the given geometric sequence. a1 = 14, r = –2, n = 11

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Gianna 3 weeks 2021-09-24T04:57:26+00:00 2 Answers 0

Answers ( )

    0
    2021-09-24T04:58:28+00:00

    Answer:

    a_{11} = 14336

    Step-by-step explanation:

    The general formula for the twelfth term of a geometric sequence is:

    a_n = a_1(r)^{n-1}

    Where a_1 is the first term and r is the common ratio

    In this case we know that:

    a_1 = 14\\r=-2

    The equation is:

    a_n = 14(-2)^{n-1}

    So for n = 11 we look for a_{11}

    a_{11} = 14(-2)^{11-1}

    a_{11} = 14(-2)^{10}

    a_{11} = 14336

    0
    2021-09-24T04:58:56+00:00

    Answer:

    11^{th} term = 14336

    Step-by-step explanation:

    We are given the first term  a _ 1 = 1 4 and  common ratio  r = - 2 of a geometric sequence and we are to find the 11^{th} term of this sequence.

    We know that the formula to find the n^{th} term in a geometric sequence is given by:

    n^{th} term =  a r ^ { n - 1 }

    Substituting the given values in the above formula:

    11^{th} term = 14 \times(-2)^{11-1}

    11^{th} term = 14 \times(-2)^{10}

    11^{th} term = 14336

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