If f(1)=7 and f(n+1)=-4f(n)-3 then find the value of f(5) Answer:

Given f(1): We are given that f(1) = 7. We need to find f(5) using the recursive formula f(n+1) = -4f(n) - 3. Let's start by finding f(2). f(2) = -4f(1) - 3 f(2) = -4(7) - 3 f(2) = -28 - 3 f(2) = -31Find f(2): Now that we have f(2), we can find f(3) using the same recursive formula. f(3) = -4f(2) - 3 f(3) = -4(-31) - 3 f(3) = 124 - 3 f(3) = 121Calculate f(3): Next, we calculate f(4) using f(3). f(4) = -4f(3) - 3 f(4) = -4(121) - 3 f(4) = -484 - 3 f(4) = -487Find f(4): Finally, we find f(5) using f(4). f(5) = -4f(4) - 3 f(5) = -4(-487) - 3 f(5) = 1948 - 3 f(5) = 1945

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
f(1)=7 and
f(n+1)=-4f(n)-3 then find the value of
f(5)
Answer:

If $f(1)=7$ and $f(n+1)=-4 f(n)-3$ then find the value of $f(5)$ $\newline$ Answer:

View step-by-step help

Full solution

Q. If

f(1)=7

and

f(n+1)=-4 f(n)-3

then find the value of

f(5)

\newline

Answer:

Given $f(1)$ : We are given that $f(1) = 7$ . We need to find $f(5)$ using the recursive formula $f(n+1) = -4f(n) - 3$ . Let's start by finding $f(2)$ . $\newline$ $f(2) = -4f(1) - 3$ $\newline$ $f(2) = -4(7) - 3$ $\newline$ $f(2) = -28 - 3$ $\newline$ $f(2) = -31$
Find $f(2)$ : Now that we have $f(2)$ , we can find $f(3)$ using the same recursive formula. $f(3) = -4f(2) - 3$ $f(3) = -4(-31) - 3$ $f(3) = 124 - 3$ $f(3) = 121$
Calculate $f(3)$ : Next, we calculate $f(4)$ using $f(3)$ .
$f(4) = -4f(3) - 3$
$f(4) = -4(121) - 3$
$f(4) = -484 - 3$
$f(4) = -487$
Find $f(4)$ : Finally, we find $f(5)$ using $f(4)$ . $f(5) = -4f(4) - 3$ $f(5) = -4(-487) - 3$ $f(5) = 1948 - 3$ $f(5) = 1945$