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

Given initial conditions: We are given the initial conditions f(1) = 0 and f(2) = 1. We need to use the recursive formula f(n) = 3f(n-1) + 3f(n-2) to find f(3).Calculate f(3): Using the recursive formula, we calculate f(3) = 3f(2) + 3f(1) = 3*1 + 3*0 = 3.Find f(4): Next, we find f(4) using the recursive formula: f(4) = 3f(3) + 3f(2) = 3*3 + 3*1 = 9 + 3 = 12.Continue with f(5): We continue with the recursive formula to find f(5): f(5) = 3f(4) + 3f(3) = 3*12 + 3*3 = 36 + 9 = 45.Use recursive formula for f(6): Finally, we use the recursive formula to find f(6): f(6) = 3f(5) + 3f(4) = 3*45 + 3*12 = 135 + 36 = 171.

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

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

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Precalculus

Find the roots of factored polynomials

Full solution

Q. If

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

and

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

then find the value of

f(6)

\newline

Answer:

Given initial conditions: We are given the initial conditions $f(1) = 0$ and $f(2) = 1$ . We need to use the recursive formula $f(n) = 3f(n-1) + 3f(n-2)$ to find $f(3)$ .
Calculate $f(3)$ : Using the recursive formula, we calculate $f(3) = 3f(2) + 3f(1) = 3\times1 + 3\times0 = 3$ .
Find $f(4)$ : Next, we find $f(4)$ using the recursive formula: $f(4) = 3f(3) + 3f(2) = 3\times3 + 3\times1 = 9 + 3 = 12$ .
Continue with $f(5)$ : We continue with the recursive formula to find $f(5)$ : $f(5) = 3f(4) + 3f(3) = 3\times12 + 3\times3 = 36 + 9 = 45$ .
Use recursive formula for $f(6)$ : Finally, we use the recursive formula to find $f(6)$ : $f(6) = 3f(5) + 3f(4) = 3\times45 + 3\times12 = 135 + 36 = 171$ .