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

Find f(3): Use the given initial conditions to find f(3). The recursive formula is f(n) = 3f(n-1) + f(n-2). We know f(1) = 4 and f(2) = 1. Calculate f(3) using the formula. f(3) = 3f(2) + f(1) = 3(1) + 4 = 3 + 4 = 7.Find f(4): Use the values of f(2) and f(3) to find f(4). We have f(2) = 1 and f(3) = 7. Calculate f(4) using the formula. f(4) = 3f(3) + f(2) = 3(7) + 1 = 21 + 1 = 22.Find f(5): Use the values of f(3) and f(4) to find f(5). We have f(3) = 7 and f(4) = 22. Calculate f(5) using the formula. f(5) = 3f(4) + f(3) = 3(22) + 7 = 66 + 7 = 73.

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

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

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 initial conditions to find $f(3)$ . The recursive formula is $f(n) = 3f(n-1) + f(n-2)$ . We know $f(1) = 4$ and $f(2) = 1$ . Calculate $f(3)$ using the formula. $f(3) = 3f(2) + f(1) = 3(1) + 4 = 3 + 4 = 7$ .
Find $f(4)$ : Use the values of $f(2)$ and $f(3)$ to find $f(4)$ . We have $f(2) = 1$ and $f(3) = 7$ . Calculate $f(4)$ using the formula. $f(4) = 3f(3) + f(2) = 3(7) + 1 = 21 + 1 = 22$ .
Find $f(5)$ : Use the values of $f(3)$ and $f(4)$ to find $f(5)$ . We have $f(3) = 7$ and $f(4) = 22$ . Calculate $f(5)$ using the formula. $f(5) = 3f(4) + f(3) = 3(22) + 7 = 66 + 7 = 73$ .