If f(1)=5,f(2)=4 and f(n)=3f(n-1)-f(n-2) then find the value of f(5). Answer:

Find f(3): Use the given recursive function and initial conditions to find f(3). The recursive function is f(n) = 3f(n-1) - f(n-2). We know f(1) = 5 and f(2) = 4. Calculate f(3) using the recursive function. f(3) = 3f(2) - f(1) = 3(4) - 5 = 12 - 5 = 7.Find f(4): Use the recursive function to find f(4). We now know f(2) = 4 and f(3) = 7. Calculate f(4) using the recursive function. f(4) = 3f(3) - f(2) = 3(7) - 4 = 21 - 4 = 17.Find f(5): Use the recursive function to find f(5). We now know f(3) = 7 and f(4) = 17. Calculate f(5) using the recursive function. f(5) = 3f(4) - f(3) = 3(17) - 7 = 51 - 7 = 44.

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If
f(1)=5,f(2)=4 and
f(n)=3f(n-1)-f(n-2) then find the value of
f(5).
Answer:

If $f(1)=5, f(2)=4$ and $f(n)=3 f(n-1)-f(n-2)$ then find the value of $f(5)$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=5, f(2)=4

and

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

then find the value of

f(5)

\newline

Answer:

Find $f(3)$ : Use the given recursive function and initial conditions to find $f(3)$ . The recursive function is $f(n) = 3f(n-1) - f(n-2)$ . We know $f(1) = 5$ and $f(2) = 4$ . Calculate $f(3)$ using the recursive function. $f(3) = 3f(2) - f(1) = 3(4) - 5 = 12 - 5 = 7$ .
Find $f(4)$ : Use the recursive function to find $f(4)$ . We now know $f(2) = 4$ and $f(3) = 7$ . Calculate $f(4)$ using the recursive function. $f(4) = 3f(3) - f(2) = 3(7) - 4 = 21 - 4 = 17$ .
Find $f(5)$ : Use the recursive function to find $f(5)$ . We now know $f(3) = 7$ and $f(4) = 17$ . Calculate $f(5)$ using the recursive function. $f(5) = 3f(4) - f(3) = 3(17) - 7 = 51 - 7 = 44$ .