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

Understand Recursive Function: Understand the given recursive function. 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 * 9 f(2) = -36Find 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 * (-36) f(3) = 144Find 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 * 144 f(4) = -576

Home

Math Problems

Grade 8

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. $f(4) = -4 \times 144$ $f(4) = -576$