If f(1)=0,f(2)=3 and f(n)=3f(n-1)-2f(n-2) then find the value of f(5). Answer:

Calculate f(3): To find f(5), we need to use the recursive formula f(n)=3f(n-1)-2f(n-2) to find the values of f(3) and f(4) first, since we already know f(1) and f(2).Calculate f(4): Let's calculate f(3) using the given formula: f(3)=3f(3-1)-2f(3-2) which simplifies to f(3)=3f(2)-2f(1).Calculate f(5): Substitute the known values f(2)=3 and f(1)=0 into the formula to get f(3)=3*3-2*0 which simplifies to f(3)=9.Now let's calculate f(4) using the formula: f(4)=3f(4-1)-2f(4-2) which simplifies to f(4)=3f(3)-2f(2).Substitute the known values f(3)=9 and f(2)=3 into the formula to get f(4)=3*9-2*3 which simplifies to f(4)=27-6, so f(4)=21.Finally, we calculate f(5) using the formula: f(5)=3f(5-1)-2f(5-2) which simplifies to f(5)=3f(4)-2f(3).Substitute the known values f(4)=21 and f(3)=9 into the formula to get f(5)=3*21-2*9 which simplifies to f(5)=63-18, so f(5)=45.

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If
f(1)=0,f(2)=3 and
f(n)=3f(n-1)-2f(n-2) then find the value of
f(5).
Answer:

If $f(1)=0, f(2)=3$ and $f(n)=3 f(n-1)-2 f(n-2)$ then find the value of $f(5)$ . $\newline$ Answer:

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Precalculus

Find the roots of factored polynomials

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Q. If

f(1)=0, f(2)=3

and

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

then find the value of

f(5)

\newline

Answer:

Calculate $f(3)$ : To find $f(5)$ , we need to use the recursive formula $f(n)=3f(n-1)-2f(n-2)$ to find the values of $f(3)$ and $f(4)$ first, since we already know $f(1)$ and $f(2)$ .
Calculate $f(4)$ : Let's calculate $f(3)$ using the given formula: $f(3)=3f(3-1)-2f(3-2)$ which simplifies to $f(3)=3f(2)-2f(1)$ .
Calculate $f(5)$ : Substitute the known values $f(2)=3$ and $f(1)=0$ into the formula to get $f(3)=3\times 3-2\times 0$ which simplifies to $f(3)=9$ .
Calculate $f(5)$ : Substitute the known values $f(2)=3$ and $f(1)=0$ into the formula to get $f(3)=3\times 3-2\times 0$ which simplifies to $f(3)=9$ .Now let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-2f(4-2)$ which simplifies to $f(4)=3f(3)-2f(2)$ .
Calculate $f(5)$ : Substitute the known values $f(2)=3$ and $f(1)=0$ into the formula to get $f(3)=3\times 3-2\times 0$ which simplifies to $f(3)=9$ .Now let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-2f(4-2)$ which simplifies to $f(4)=3f(3)-2f(2)$ .Substitute the known values $f(3)=9$ and $f(2)=3$ into the formula to get $f(2)=3$ $0$ which simplifies to $f(2)=3$ $1$ , so $f(2)=3$ $2$ .
Calculate $f(5)$ : Substitute the known values $f(2)=3$ and $f(1)=0$ into the formula to get $f(3)=3\times 3-2\times 0$ which simplifies to $f(3)=9$ .Now let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-2f(4-2)$ which simplifies to $f(4)=3f(3)-2f(2)$ .Substitute the known values $f(3)=9$ and $f(2)=3$ into the formula to get $f(2)=3$ $0$ which simplifies to $f(2)=3$ $1$ , so $f(2)=3$ $2$ .Finally, we calculate $f(5)$ using the formula: $f(2)=3$ $4$ which simplifies to $f(2)=3$ $5$ .
Calculate $f(5)$ : Substitute the known values $f(2)=3$ and $f(1)=0$ into the formula to get $f(3)=3\times 3-2\times 0$ which simplifies to $f(3)=9$ .Now let's calculate $f(4)$ using the formula: $f(4)=3f(4-1)-2f(4-2)$ which simplifies to $f(4)=3f(3)-2f(2)$ .Substitute the known values $f(3)=9$ and $f(2)=3$ into the formula to get $f(2)=3$ $0$ which simplifies to $f(2)=3$ $1$ , so $f(2)=3$ $2$ .Finally, we calculate $f(5)$ using the formula: $f(2)=3$ $4$ which simplifies to $f(2)=3$ $5$ .Substitute the known values $f(2)=3$ $2$ and $f(3)=9$ into the formula to get $f(2)=3$ $8$ which simplifies to $f(2)=3$ $9$ , so $f(1)=0$ $0$ .