If f(1)=9 and f(n)=3f(n-1)-n then find the value of f(3). Answer:

Understand the recursive function: Understand the recursive function. The function f(n) is defined recursively, meaning that to find f(n), we need to know the value of f(n-1). We are given that f(1) = 9, and we want to find f(3).Find f(2) using formula: Find the value of f(2) using the recursive formula. We use the recursive formula f(n) = 3f(n-1) - n with n = 2. f(2) = 3f(2-1) - 2 f(2) = 3f(1) - 2 Since we know f(1) = 9, we substitute that value in. f(2) = 3(9) - 2 f(2) = 27 - 2 f(2) = 25Find f(3) using formula: Find the value of f(3) using the recursive formula. Now we use the recursive formula again with n = 3. f(3) = 3f(3-1) - 3 f(3) = 3f(2) - 3 We found f(2) = 25 in the previous step, so we substitute that value in. f(3) = 3(25) - 3 f(3) = 75 - 3 f(3) = 72

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If
f(1)=9 and
f(n)=3f(n-1)-n then find the value of
f(3).
Answer:

If $f(1)=9$ and $f(n)=3 f(n-1)-n$ then find the value of $f(3)$ . $\newline$ Answer:

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Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=9

and

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

then find the value of

f(3)

\newline

Answer:

Understand the recursive function: Understand the recursive function. $\newline$ The function $f(n)$ is defined recursively, meaning that to find $f(n)$ , we need to know the value of $f(n-1)$ . We are given that $f(1) = 9$ , and we want to find $f(3)$ .
Find $f(2)$ using formula: Find the value of $f(2)$ using the recursive formula. $\newline$ We use the recursive formula $f(n) = 3f(n-1) - n$ with $n = 2$ . $\newline$ $f(2) = 3f(2-1) - 2$ $\newline$ $f(2) = 3f(1) - 2$ $\newline$ Since we know $f(1) = 9$ , we substitute that value in. $\newline$ $f(2) = 3(9) - 2$ $\newline$ $f(2) = 27 - 2$ $\newline$ $f(2) = 25$
Find $f(3)$ using formula: Find the value of $f(3)$ using the recursive formula. $\newline$ Now we use the recursive formula again with $n = 3$ . $\newline$ $f(3) = 3f(3-1) - 3$ $\newline$ $f(3) = 3f(2) - 3$ $\newline$ We found $f(2) = 25$ in the previous step, so we substitute that value in. $\newline$ $f(3) = 3(25) - 3$ $\newline$ $f(3) = 75 - 3$ $\newline$ $f(3) = 72$