*****SHOW WORK pleaseeee*** ASAP ANSWERRR If a sequence is defined recursively by f(0)=4 and f(n+1)= -3f(n)+1 for n≥0, the f(3) i

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*****SHOW WORK pleaseeee***

ASAP ANSWERRR If a sequence is defined recursively by f(0)=4 and f(n+1)= -3f(n)+1 for n≥0, the f(3) is equal to
1. -11

2. -8

3. -101

4. 34

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Hadley 2 months 2021-11-30T21:47:33+00:00 1 Answer 0 views 0

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    2021-11-30T21:49:16+00:00

    Option 3 : f(3)=-101 is the correct answer.

    Explanation:

    It is given that the recursive equation is f(n+1)=-3f(n)+1 and also $f(0)=4$

    To determine the value of f(3), we need to know the previous terms.

    Thus, let us substitute n=0,1,2 in the equation f(n+1)=-3f(n)+1

    For n=0, we get,

    $\begin{aligned} f(0+1) &=-3 f(0)+1 \\ f(1) &=-3(4)+1 \\ f(1) &=-12+1 \\ f(1) &=-11 \end{aligned}$

    For n=1, we get,

    $\begin{aligned} f(1+1) &=-3(-11)+1 \\ f(2) &=33+1 \\ f(2) &=34\end{aligned}$

    For n=2, we get,

    $\begin{aligned} f(2+1) &=-3(34)+1 \\ f(3) &=-102+1 \\ f(3) &=-101 \end{aligned}$

    Thus, the value of f(3) is -101.

    Hence, Option 3 is the correct answer.

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