Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
f(1)=9 and
f(n)=-4f(n-1) then find the value of
f(4).
Answer:

If $f(1)=9$ and $f(n)=-4 f(n-1)$ then find the value of $f(4)$ . $\newline$ Answer:

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. If

f(1)=9

and

f(n)=-4 f(n-1)

then find the value of

f(4)

.

\newline

Answer:

Understand Recursive Function: Understand the given recursive function. $\newline$ The function $f(n)$ is defined recursively, meaning that the value of the function at $n$ depends on the value of the function at $n-1$ . We are given that $f(1) = 9$ and that $f(n) = -4f(n-1)$ for any $n > 1$ .
Find $f(2)$ : Find the value of $f(2)$ . Using the recursive formula $f(n) = -4f(n-1)$ , we substitute $n$ with $2$ to find $f(2)$ . $f(2) = -4f(2-1)$ $f(2) = -4f(1)$ Since we know $f(1) = 9$ , we can substitute that value in. $f(2) = -4 \times 9$ $f(2)$ $0$
Find $f(3)$ : Find the value of $f(3)$ . Using the recursive formula again, we substitute $n$ with $3$ to find $f(3)$ . $f(3) = -4f(3-1)$ $f(3) = -4f(2)$ We found $f(2) = -36$ in the previous step, so we substitute that value in. $f(3) = -4 \times (-36)$ $f(3) = 144$
Find $f(4)$ : Find the value of $f(4)$ . Using the recursive formula one last time, we substitute $n$ with $4$ to find $f(4)$ . $f(4) = -4f(4-1)$ $f(4) = -4f(3)$ We found $f(3) = 144$ in the previous step, so we substitute that value in. $f(4) = -4 \times 144$ $f(4) = -576$

More problems from Write and solve direct variation equations

Question

(x-3)(a x+4)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=3

x=-2

, what is the value of

a

Posted 1 month ago

Question

3 x^{2}+a x-5=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=-5

x=\frac{1}{3}

, what is the value of

a

Posted 27 days ago

Question

a x^{2}+5 x+2=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=-2

x=-\frac{1}{2}

, what is the value of

a

Posted 2 months ago

Question

Find the average value of the function

f(x)=\frac{2}{x-11}

x=2

x=8

. Express your answer as a constant times

\ln 3

\newline

\square \ln 3

Posted 2 months ago

Question

6+\frac{4}{a}+\frac{b}{3}

a=4

b=3

Posted 2 months ago

Question

4 x-32 k x=53

\newline

In the given equation,

k

is a constant. The equation has no solution. What is the value of

k

Posted 2 months ago

Question

a_{1}=9

a_{n+1}=2 a_{n}+2

then find the value of

a_{5}

\newline

Posted 2 months ago

Question

a_{1}=4

a_{n}=5 a_{n-1}-n

then find the value of

a_{5}

\newline

Posted 2 months ago

Question

a_{1}=1

a_{n}=n a_{n-1}+4

then find the value of

a_{5}

\newline

Posted 2 months ago

Question

a_{1}=9

a_{n}=n a_{n-1}-2

then find the value of

a_{5}

\newline

Posted 2 months ago