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

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

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Write and solve direct variation equations

Full solution

Q. If

f(1)=0, f(2)=5

and

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

then find the value of

f(5)

.

\newline

Answer:

Find $f(3)$ : Use the initial conditions to find $f(3)$ . The recursive formula is $f(n) = 2f(n-1) - 2f(n-2)$ . We know $f(1) = 0$ and $f(2) = 5$ . Now calculate $f(3)$ using the formula. $f(3) = 2f(2) - 2f(1) = 2\times 5 - 2\times 0 = 10 - 0 = 10$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We have $f(2) = 5$ and $f(3) = 10$ . Now calculate $f(4)$ using the formula. $f(4) = 2f(3) - 2f(2) = 2\times10 - 2\times5 = 20 - 10 = 10$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We have $f(3) = 10$ and $f(4) = 10$ . Now calculate $f(5)$ using the formula. $f(5) = 2f(4) - 2f(3) = 2\times10 - 2\times10 = 20 - 20 = 0$ .

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