If f(1)=5,f(2)=0 and f(n)=3f(n-1)-f(n-2) then find the value of f(6). Answer:

Find f(3): Use the given recursive formula to find f(3). The recursive formula is f(n) = 3f(n-1) - f(n-2). We know f(1) = 5 and f(2) = 0. Calculate f(3) using the formula. f(3) = 3f(2) - f(1) = 3*0 - 5 = -5.Find f(4): Use the recursive formula to find f(4). We now know f(2) = 0 and f(3) = -5. Calculate f(4) using the formula. f(4) = 3f(3) - f(2) = 3*(-5) - 0 = -15.Find f(5): Use the recursive formula to find f(5). We now know f(3) = -5 and f(4) = -15. Calculate f(5) using the formula. f(5) = 3f(4) - f(3) = 3*(-15) - (-5) = -45 + 5 = -40.Find f(6): Use the recursive formula to find f(6). We now know f(4) = -15 and f(5) = -40. Calculate f(6) using the formula. f(6) = 3f(5) - f(4) = 3*(-40) - (-15) = -120 + 15 = -105.

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If
f(1)=5,f(2)=0 and
f(n)=3f(n-1)-f(n-2) then find the value of
f(6).
Answer:

If $f(1)=5, f(2)=0$ and $f(n)=3 f(n-1)-f(n-2)$ 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)=5, f(2)=0

and

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

then find the value of

f(6)

\newline

Answer:

Find $f(3)$ : Use the given recursive formula to find $f(3)$ . The recursive formula is $f(n) = 3f(n-1) - f(n-2)$ . We know $f(1) = 5$ and $f(2) = 0$ . Calculate $f(3)$ using the formula. $f(3) = 3f(2) - f(1) = 3\times 0 - 5 = -5$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We now know $f(2) = 0$ and $f(3) = -5$ . Calculate $f(4)$ using the formula. $f(4) = 3f(3) - f(2) = 3*(-5) - 0 = -15$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We now know $f(3) = -5$ and $f(4) = -15$ . Calculate $f(5)$ using the formula. $f(5) = 3f(4) - f(3) = 3*(-15) - (-5) = -45 + 5 = -40$ .
Find $f(6)$ : Use the recursive formula to find $f(6)$ . We now know $f(4) = -15$ and $f(5) = -40$ . Calculate $f(6)$ using the formula. $f(6) = 3f(5) - f(4) = 3*(-40) - (-15) = -120 + 15 = -105$ .