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

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

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Write and solve direct variation equations

Full solution

Q. If

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

and

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

then find the value of

f(4)

.

\newline

Answer:

Find $f(3)$ : Use the given recursive function to find $f(3)$ . The recursive function is $f(n) = f(n-1) + 2f(n-2)$ . We have $f(1) = 4$ and $f(2) = 2$ . Calculate $f(3)$ using the values of $f(1)$ and $f(2)$ . $f(3) = f(3-1) + 2f(3-2) = f(2) + 2f(1) = 2 + 2(4) = 2 + 8 = 10$
Calculate $f(3)$ : Use the recursive function to find $f(4)$ . $\newline$ Now that we have $f(3) = 10$ and $f(2) = 2$ , we can find $f(4)$ . $\newline$ $f(4) = f(4-1) + 2f(4-2) = f(3) + 2f(2) = 10 + 2(2) = 10 + 4 = 14$

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