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If
f(1)=1,f(2)=0 and
f(n)=f(n-1)-3f(n-2) then find the value of
f(6).
Answer:

If $f(1)=1, f(2)=0$ and $f(n)=f(n-1)-3 f(n-2)$ then find the value of $f(6)$ . $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. If

f(1)=1, f(2)=0

and

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

then find the value of

f(6)

.

\newline

Answer:

Find $f(3)$ : Use the initial conditions to find $f(3)$ . The recursive formula is $f(n) = f(n-1) - 3f(n-2)$ . We know $f(1) = 1$ and $f(2) = 0$ . So, $f(3) = f(2) - 3f(1) = 0 - 3(1) = -3$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . $\newline$ Now we have $f(2) = 0$ and $f(3) = -3$ . $\newline$ So, $f(4) = f(3) - 3f(2) = -3 - 3(0) = -3$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We have $f(3) = -3$ and $f(4) = -3$ . So, $f(5) = f(4) - 3f(3) = -3 - 3(-3) = -3 + 9 = 6$ .
Find $f(6)$ : Use the recursive formula to find $f(6)$ . We have $f(4) = -3$ and $f(5) = 6$ . So, $f(6) = f(5) - 3f(4) = 6 - 3(-3) = 6 + 9 = 15$ .

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