If f(1)=8f(1)=8 and f(n)=4f(n-1)+1f(n)=4f(n−1)+1 then find the value of f(4)f(4).

Question

If f(1)=8f(1)=8 and f(n)=4f(n-1)+1f(n)=4f(n−1)+1 then find the value of f(4)f(4).

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Melanie 7 months 2021-10-04T04:43:48+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-04T04:44:50+00:00

    Answer:

    f(4) = 533

    Step-by-step explanation:

    The sequence in this problem is defined as:

    [tex]f(n)=4f(n-1)+1[/tex]

    where

    [tex]f(n)[/tex] is the nth-term of the sequence

    [tex]f(n-1)[/tex] is the (n-1)th term of the sequence

    Here we also know that

    [tex]f(1)=8[/tex]

    Therefore, we can find the following terms of the sequence by substituting the output of the previous term in the sequence. For instance, the term f(2) is calculated by substituting 8 into f(n-1). Then we find:

    [tex]f(2)=4f(2-1)+1=4f(1)+1=4\cdot 8+1=33[/tex]

    [tex]f(3)=4f(2)+1=4\cdot 33+1=133[/tex]

    [tex]f(4)=4f(3)+1=4\cdot 133 +1=533[/tex]

    So, the term f(4) is 533.

    0
    2021-10-04T04:45:24+00:00

    Answer:

    f(4) = 533

    Step-by-step explanation:

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45:7+7-4:2-5:5*4+35:2 =? ( )