Find the explicit formula for the given sequence. -4, 12, -36, 108

Question

Find the explicit formula for the given sequence.
-4, 12, -36, 108

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Brielle 2 weeks 2021-09-12T07:23:47+00:00 1 Answer 0

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    2021-09-12T07:24:58+00:00

    The required explicit formula is a_n = -3(a_{n - 1})

    Solution:

    Given that sequence is -4, 12, -36, 108

    To find: explicit formula

    Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence

    An explicit formula designates the nth term of the sequence, as an expression of n (where n = the term’s location). It defines the sequence as a formula in terms of n.

    Let us first find the logic used in sequence

    \begin{array}{l}{-4 \times-3=12} \\\\ {12 \times-3=-36} \\\\ {-36 \times-3=108}\end{array}

    So we can see clearly that next term in sequence is obtained by multiplying -3 with previous term

    This can be defined in terms of “n”

    a_n = -3(a_{n - 1})

    Where a_n represents the next terms location and a_{n-1} represents previous term location

    So the required explicit formula is a_n = -3(a_{n - 1})

    Let us verify our explicit formula

    Now let us find the 4th term of sequence

    \text {so } a_{n}=a_{4} \text { and } a_{n-1}=a_{4-1}=a_{3}

    a_{4}=-3\left(a_{3}\right)=-3(-36)=108

    Thus using the explicit formula, next terms in sequence can be found

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