If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?

Question

If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?

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Julia 11 mins 2021-09-15T02:17:29+00:00 2 Answers 0

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    0
    2021-09-15T02:18:42+00:00

    f(1)=160\\f(n+1)=-2f(n)\\\\f(2)=-2\cdot 160=-320\\f(3)=-2\cdot(-320)=640\\f(4)=-2\cdot 640=-1280

    0
    2021-09-15T02:18:44+00:00

    Answer:

    -1280

    Step-by-step explanation:

    There are 2 ways you could do this. You could just do the question until you come to the end of f(4). That is likely the simplest way to do it.

    f(1) = 160

    f(2) = – 2 * f(1)

    f(2) = -2*160

    f(2) = -320

    f(3) = -2 * f(2)

    f(3) = -2 * – 320

    f(3) = 640

    f(4) = – 2 * f(3)

    f(4) = – 2 * 640

    f(4) = – 1280

    I don’t know that you could do this explicitly with any real confidence.

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