If f(1)=5,f(2)=2 and f(n)=3f(n-1)-3f(n-2) then find the value of f(6). Answer:

Calculate f(3): To find f(6), we need to use the recursive formula f(n)=3f(n-1)-3f(n-2) to calculate the values of f(3), f(4), and f(5) first.Calculate f(4): Let's calculate f(3) using the given formula: f(3)=3f(3-1)-3f(3-2) which simplifies to f(3)=3f(2)-3f(1).Calculate f(5): Substitute the known values of f(2) and f(1) into the formula: f(3)=3*2-3*5 which simplifies to f(3)=6-15.Calculate f(6): Calculate the value of f(3): f(3)=-9.Now, let's calculate f(4) using the formula: f(4)=3f(4-1)-3f(4-2) which simplifies to f(4)=3f(3)-3f(2).Substitute the known values of f(3) and f(2) into the formula: f(4)=3*(-9)-3*2 which simplifies to f(4)=-27-6.Calculate the value of f(4): f(4)=-33.Next, calculate f(5) using the formula: f(5)=3f(5-1)-3f(5-2) which simplifies to f(5)=3f(4)-3f(3).Substitute the known values of f(4) and f(3) into the formula: f(5)=3*(-33)-3*(-9) which simplifies to f(5)=-99+27.Calculate the value of f(5): f(5)=-72.Finally, calculate f(6) using the formula: f(6)=3f(6-1)-3f(6-2) which simplifies to f(6)=3f(5)-3f(4).Substitute the known values of f(5) and f(4) into the formula: f(6)=3*(-72)-3*(-33) which simplifies to f(6)=-216+99.Calculate the value of f(6): f(6)=-117.

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If
f(1)=5,f(2)=2 and
f(n)=3f(n-1)-3f(n-2) then find the value of
f(6).
Answer:

If $f(1)=5, f(2)=2$ 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)=5, f(2)=2

and

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

then find the value of

f(6)

\newline

Answer:

Calculate $f(3)$ : To find $f(6)$ , we need to use the recursive formula $f(n)=3f(n-1)-3f(n-2)$ to calculate the values of $f(3)$ , $f(4)$ , and $f(5)$ first.
Calculate $f(4)$ : Let's calculate $f(3)$ using the given formula: $f(3)=3f(3-1)-3f(3-2)$ which simplifies to $f(3)=3f(2)-3f(1)$ .
Calculate $f(5)$ : Substitute the known values of $f(2)$ and $f(1)$ into the formula: $f(3)=3\times 2-3\times 5$ which simplifies to $f(3)=6-15$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .Next, calculate $f(3)$ $2$ using the formula: $f(3)$ $3$ which simplifies to $f(3)$ $4$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .Next, calculate $f(3)$ $2$ using the formula: $f(3)$ $3$ which simplifies to $f(3)$ $4$ .Substitute the known values of $f(4)$ and $f(3)$ into the formula: $f(3)$ $7$ which simplifies to $f(3)$ $8$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .Next, calculate $f(3)$ $2$ using the formula: $f(3)$ $3$ which simplifies to $f(3)$ $4$ .Substitute the known values of $f(4)$ and $f(3)$ into the formula: $f(3)$ $7$ which simplifies to $f(3)$ $8$ .Calculate the value of $f(3)$ $2$ : $f(3)=-9$ $0$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .Next, calculate $f(3)$ $2$ using the formula: $f(3)$ $3$ which simplifies to $f(3)$ $4$ .Substitute the known values of $f(4)$ and $f(3)$ into the formula: $f(3)$ $7$ which simplifies to $f(3)$ $8$ .Calculate the value of $f(3)$ $2$ : $f(3)=-9$ $0$ .Finally, calculate $f(6)$ using the formula: $f(3)=-9$ $2$ which simplifies to $f(3)=-9$ $3$ .
Calculate $f(6)$ : Calculate the value of $f(3)$ : $f(3)=-9$ .Now, let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of $f(3)$ and $f(2)$ into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of $f(4)$ : $f(3)$ $1$ .Next, calculate $f(3)$ $2$ using the formula: $f(3)$ $3$ which simplifies to $f(3)$ $4$ .Substitute the known values of $f(4)$ and $f(3)$ into the formula: $f(3)$ $7$ which simplifies to $f(3)$ $8$ .Calculate the value of $f(3)$ $2$ : $f(3)=-9$ $0$ .Finally, calculate $f(6)$ using the formula: $f(3)=-9$ $2$ which simplifies to $f(3)=-9$ $3$ .Substitute the known values of $f(3)$ $2$ and $f(4)$ into the formula: $f(3)=-9$ $6$ which simplifies to $f(3)=-9$ $7$ .
Calculate f( $6$ ): Calculate the value of f( $3$ ): $f(3)=-9$ .Now, let's calculate f( $4$ ) using the formula: $f(4)=3f(4-1)-3f(4-2)$ which simplifies to $f(4)=3f(3)-3f(2)$ .Substitute the known values of f( $3$ ) and f( $2$ ) into the formula: $f(4)=3*(-9)-3*2$ which simplifies to $f(4)=-27-6$ .Calculate the value of f( $4$ ): $f(4)=-33$ .Next, calculate f( $5$ ) using the formula: $f(5)=3f(5-1)-3f(5-2)$ which simplifies to $f(5)=3f(4)-3f(3)$ .Substitute the known values of f( $4$ ) and f( $3$ ) into the formula: $f(5)=3*(-33)-3*(-9)$ which simplifies to $f(5)=-99+27$ .Calculate the value of f( $5$ ): $f(4)=3f(4-1)-3f(4-2)$ $0$ .Finally, calculate f( $6$ ) using the formula: $f(4)=3f(4-1)-3f(4-2)$ $1$ which simplifies to $f(4)=3f(4-1)-3f(4-2)$ $2$ .Substitute the known values of f( $5$ ) and f( $4$ ) into the formula: $f(4)=3f(4-1)-3f(4-2)$ $3$ which simplifies to $f(4)=3f(4-1)-3f(4-2)$ $4$ .Calculate the value of f( $6$ ): $f(4)=3f(4-1)-3f(4-2)$ $5$ .

If $f(1)=5, f(2)=2$ and $f(n)=3 f(n-1)-3 f(n-2)$ then find the value of $f(6)$ . $\newline$ Answer:

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