If f(1)=0,f(2)=3 and f(n)=2f(n-1)-f(n-2) then find the value of f(6). Answer:

Find f(3): Use the given initial conditions to find f(3). The recursive formula is f(n) = 2f(n-1) - f(n-2). We know f(1) = 0 and f(2) = 3. Calculate f(3) using the formula. f(3) = 2f(2) - f(1) = 2*3 - 0 = 6.Find f(4): Use the recursive formula to find f(4). We now have f(2) = 3 and f(3) = 6. Calculate f(4) using the formula. f(4) = 2f(3) - f(2) = 2*6 - 3 = 12 - 3 = 9.Find f(5): Use the recursive formula to find f(5). We now have f(3) = 6 and f(4) = 9. Calculate f(5) using the formula. f(5) = 2f(4) - f(3) = 2*9 - 6 = 18 - 6 = 12.Find f(6): Use the recursive formula to find f(6). We now have f(4) = 9 and f(5) = 12. Calculate f(6) using the formula. f(6) = 2f(5) - f(4) = 2*12 - 9 = 24 - 9 = 15.

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If
f(1)=0,f(2)=3 and
f(n)=2f(n-1)-f(n-2) then find the value of
f(6).
Answer:

If $f(1)=0, f(2)=3$ and $f(n)=2 f(n-1)-f(n-2)$ then find the value of $f(6)$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=0, f(2)=3

and

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

then find the value of

f(6)

\newline

Answer:

Find $f(3)$ : Use the given initial conditions to find $f(3)$ . The recursive formula is $f(n) = 2f(n-1) - f(n-2)$ . We know $f(1) = 0$ and $f(2) = 3$ . Calculate $f(3)$ using the formula. $f(3) = 2f(2) - f(1) = 2\times3 - 0 = 6$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We now have $f(2) = 3$ and $f(3) = 6$ . Calculate $f(4)$ using the formula. $f(4) = 2f(3) - f(2) = 2\times6 - 3 = 12 - 3 = 9$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We now have $f(3) = 6$ and $f(4) = 9$ . Calculate $f(5)$ using the formula. $f(5) = 2f(4) - f(3) = 2\times9 - 6 = 18 - 6 = 12$ .
Find $f(6)$ : Use the recursive formula to find $f(6)$ . We now have $f(4) = 9$ and $f(5) = 12$ . Calculate $f(6)$ using the formula. $f(6) = 2f(5) - f(4) = 2\times12 - 9 = 24 - 9 = 15$ .