Question

*****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

Answer 1

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.