If f(1)=2,f(2)=5 and f(n)=f(n-1)+3f(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) = f(n-1) + 3f(n-2). We know f(1) = 2 and f(2) = 5. Now calculate f(3) using the formula. f(3) = f(2) + 3f(1) = 5 + 3(2) = 5 + 6 = 11.Find f(4): Use the recursive formula to find f(4). We have f(2) = 5 and f(3) = 11. Now calculate f(4) using the formula. f(4) = f(3) + 3f(2) = 11 + 3(5) = 11 + 15 = 26.Find f(5): Use the recursive formula to find f(5). We have f(3) = 11 and f(4) = 26. Now calculate f(5) using the formula. f(5) = f(4) + 3f(3) = 26 + 3(11) = 26 + 33 = 59.

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

If $f(1)=2, f(2)=5$ and $f(n)=f(n-1)+3 f(n-2)$ 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)=2, f(2)=5

and

f(n)=f(n-1)+3 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 $f(n) = f(n-1) + 3f(n-2)$ . We know $f(1) = 2$ and $f(2) = 5$ . Now calculate $f(3)$ using the formula. $f(3) = f(2) + 3f(1) = 5 + 3(2) = 5 + 6 = 11$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We have $f(2) = 5$ and $f(3) = 11$ . Now calculate $f(4)$ using the formula. $f(4) = f(3) + 3f(2) = 11 + 3(5) = 11 + 15 = 26$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We have $f(3) = 11$ and $f(4) = 26$ . Now calculate $f(5)$ using the formula. $f(5) = f(4) + 3f(3) = 26 + 3(11) = 26 + 33 = 59$ .