If f(1)=1,f(2)=4 and f(n)=f(n-1)-3f(n-2) then find the value of f(6). Answer:

Find f(3): Use the given initial conditions to find f(3). The recursive formula is f(n) = f(n-1) - 3f(n-2). We know f(1) = 1 and f(2) = 4. Calculate f(3) using the formula. f(3) = f(2) - 3f(1) = 4 - 3(1) = 4 - 3 = 1.Find f(4): Use the recursive formula to find f(4). Now that we have f(3), we can find f(4). f(4) = f(3) - 3f(2) = 1 - 3(4) = 1 - 12 = -11.Find f(5): Use the recursive formula to find f(5). With f(4) found, we can now find f(5). f(5) = f(4) - 3f(3) = -11 - 3(1) = -11 - 3 = -14.Find f(6): Finally, use the recursive formula to find f(6). Now we can find f(6) using f(5) and f(4). f(6) = f(5) - 3f(4) = -14 - 3(-11) = -14 + 33 = 19.

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If
f(1)=1,f(2)=4 and
f(n)=f(n-1)-3f(n-2) then find the value of
f(6).
Answer:

If $f(1)=1, f(2)=4$ and $f(n)=f(n-1)-3 f(n-2)$ then find the value of $f(6)$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=1, f(2)=4

and

f(n)=f(n-1)-3 f(n-2)

then find the value of

f(6)

\newline

Answer:

Find $f(3)$ : Use the given initial conditions to find $f(3)$ . The recursive formula is $f(n) = f(n-1) - 3f(n-2)$ . We know $f(1) = 1$ and $f(2) = 4$ . Calculate $f(3)$ using the formula. $f(3) = f(2) - 3f(1) = 4 - 3(1) = 4 - 3 = 1$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . $\newline$ Now that we have $f(3)$ , we can find $f(4)$ . $\newline$ $f(4) = f(3) - 3f(2) = 1 - 3(4) = 1 - 12 = -11$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . With $f(4)$ found, we can now find $f(5)$ . $f(5) = f(4) - 3f(3) = -11 - 3(1) = -11 - 3 = -14$ .
Find $f(6)$ : Finally, use the recursive formula to find $f(6)$ . Now we can find $f(6)$ using $f(5)$ and $f(4)$ . $f(6) = f(5) - 3f(4) = -14 - 3(-11) = -14 + 33 = 19$ .