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

Find f(3): Use the initial conditions to find f(3). The recursive formula is f(n) = f(n-1) - 3f(n-2). We know f(1) = 3 and f(2) = 1. Calculate f(3) using the formula. f(3) = f(2) - 3f(1) = 1 - 3(3) = 1 - 9 = -8.Find f(4): Use the recursive formula to find f(4). We now have f(2) = 1 and f(3) = -8. Calculate f(4) using the formula. f(4) = f(3) - 3f(2) = -8 - 3(1) = -8 - 3 = -11.Find f(5): Use the recursive formula to find f(5). We now have f(3) = -8 and f(4) = -11. Calculate f(5) using the formula. f(5) = f(4) - 3f(3) = -11 - 3(-8) = -11 + 24 = 13.Find f(6): Use the recursive formula to find f(6). We now have f(4) = -11 and f(5) = 13. Calculate f(6) using the formula. f(6) = f(5) - 3f(4) = 13 - 3(-11) = 13 + 33 = 46.

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

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

and

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

then find the value of

f(6)

\newline

Answer:

Find $f(3)$ : Use the initial conditions to find $f(3)$ . The recursive formula is $f(n) = f(n-1) - 3f(n-2)$ . We know $f(1) = 3$ and $f(2) = 1$ . Calculate $f(3)$ using the formula. $f(3) = f(2) - 3f(1) = 1 - 3(3) = 1 - 9 = -8$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We now have $f(2) = 1$ and $f(3) = -8$ . Calculate $f(4)$ using the formula. $f(4) = f(3) - 3f(2) = -8 - 3(1) = -8 - 3 = -11$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . We now have $f(3) = -8$ and $f(4) = -11$ . Calculate $f(5)$ using the formula. $f(5) = f(4) - 3f(3) = -11 - 3(-8) = -11 + 24 = 13$ .
Find $f(6)$ : Use the recursive formula to find $f(6)$ . We now have $f(4) = -11$ and $f(5) = 13$ . Calculate $f(6)$ using the formula. $f(6) = f(5) - 3f(4) = 13 - 3(-11) = 13 + 33 = 46$ .