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

Find f(3): Use the given recursive formula to find f(3). The recursive formula is f(n) = 3f(n-1) - 2f(n-2). We know f(1) = 2 and f(2) = 5. Calculate f(3) using f(2) and f(1). f(3) = 3f(2) - 2f(1) = 3*5 - 2*2 = 15 - 4 = 11.Find f(4): Use the recursive formula to find f(4). Now that we have f(3), we can use it along with f(2) to find f(4). f(4) = 3f(3) - 2f(2) = 3*11 - 2*5 = 33 - 10 = 23.Find f(5): Use the recursive formula to find f(5). Now that we have f(4) and f(3), we can find f(5). f(5) = 3f(4) - 2f(3) = 3*23 - 2*11 = 69 - 22 = 47.

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

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

and

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

then find the value of

f(5)

\newline

Answer:

Find $f(3)$ : Use the given recursive formula to find $f(3)$ . The recursive formula is $f(n) = 3f(n-1) - 2f(n-2)$ . We know $f(1) = 2$ and $f(2) = 5$ . Calculate $f(3)$ using $f(2)$ and $f(1)$ . $f(3) = 3f(2) - 2f(1) = 3\times5 - 2\times2 = 15 - 4 = 11$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . Now that we have $f(3)$ , we can use it along with $f(2)$ to find $f(4)$ . $f(4) = 3f(3) - 2f(2) = 3\times11 - 2\times5 = 33 - 10 = 23$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . $\newline$ Now that we have $f(4)$ and $f(3)$ , we can find $f(5)$ . $\newline$ $f(5) = 3f(4) - 2f(3) = 3\times23 - 2\times11 = 69 - 22 = 47$ .