If f(1)=4,f(2)=5 and f(n)=2f(n-1)+2f(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) = 2f(n-1) + 2f(n-2). We know f(1) = 4 and f(2) = 5. Calculate f(3) using the formula. f(3) = 2f(2) + 2f(1) = 2*5 + 2*4 = 10 + 8 = 18.Calculate f(4): Use the recursive formula to find f(4). We now have f(2) = 5 and f(3) = 18. Calculate f(4) using the formula. f(4) = 2f(3) + 2f(2) = 2*18 + 2*5 = 36 + 10 = 46.Determine f(5): Use the recursive formula to find f(5). We now have f(3) = 18 and f(4) = 46. Calculate f(5) using the formula. f(5) = 2f(4) + 2f(3) = 2*46 + 2*18 = 92 + 36 = 128.

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

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

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=4, 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 given initial conditions to find $f(3)$ . The recursive formula is $f(n) = 2f(n-1) + 2f(n-2)$ . We know $f(1) = 4$ and $f(2) = 5$ . Calculate $f(3)$ using the formula. $f(3) = 2f(2) + 2f(1) = 2\times 5 + 2\times 4 = 10 + 8 = 18$ .
Calculate $f(4)$ : Use the recursive formula to find $f(4)$ . We now have $f(2) = 5$ and $f(3) = 18$ . Calculate $f(4)$ using the formula. $f(4) = 2f(3) + 2f(2) = 2\times18 + 2\times5 = 36 + 10 = 46$ .
Determine $f(5)$ : Use the recursive formula to find $f(5)$ . We now have $f(3) = 18$ and $f(4) = 46$ . Calculate $f(5)$ using the formula. $f(5) = 2f(4) + 2f(3) = 2\times46 + 2\times18 = 92 + 36 = 128$ .