–81, 108, –144, 192, … Which formula can be used to describe the sequence? f(x) = –81(four-thirds) Superscript x m

Question

–81, 108, –144, 192, …

Which formula can be used to describe the sequence?

f(x) = –81(four-thirds) Superscript x minus 1
f(x) = –81(negative three-fourths) Superscript x minus 1
f(x) = –81(negative four-thirds) Superscript x minus 1
f(x) = –81(three-fourths) Superscript x minus 1

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Melanie 3 weeks 2021-09-28T02:57:06+00:00 2 Answers 0

Answers ( )

    0
    2021-09-28T02:58:49+00:00

    Answer:

    The formula which can be used to describe the sequence is:

    f(x)=-81(\frac{-4}{3})^{x-1}3rd answer

    Step-by-step explanation:

    The terms of the sequence are -81, 108, -144, 192, …

    ∵ 108 ÷ -81 = -\frac{4}{3}

    ∵ -144 ÷ 108 = -\frac{4}{3}

    ∵ 192 ÷ -144 =  -\frac{4}{3}

    – There is a constant ratio between each two consecutive terms

    ∴ The sequence is a geometric sequence

    The formula of the nth term of the geometric sequence is a_{n}=ar^{n-1}, where a is the first term and r is the constant ratio between each two consecutive terms

    ∵ The first term is -81

    ∴ a = -81

    ∵ The constant ratio =  -\frac{4}{3}

    ∴ r =  -\frac{4}{3}

    – Substitute then in the formula above

    ∴  a_{n}=-81(\frac{-4}{3})^{n-1}

    Assume that a_{n} = f(x)

    ∴ n = x

    ∴  f(x)=-81(\frac{-4}{3})^{x-1}

    The formula which can be used to describe the sequence is:

    f(x)=-81(\frac{-4}{3})^{x-1}

    0
    2021-09-28T02:58:55+00:00

    Answer:

    c on edge

    Step-by-step explanation:

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