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

Find f(3): Use the initial conditions to find f(3). The recursive formula is f(n) = f(n-1) - f(n-2). We know f(1) = 2 and f(2) = 1. So, f(3) = f(2) - f(1) = 1 - 2 = -1.Find f(4): Use the recursive formula to find f(4). Now we have f(2) = 1 and f(3) = -1. So, f(4) = f(3) - f(2) = -1 - 1 = -2.Find f(5): Use the recursive formula to find f(5). Now we have f(3) = -1 and f(4) = -2. So, f(5) = f(4) - f(3) = -2 - (-1) = -2 + 1 = -1.

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

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

and

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

then find the value of

f(5)

\newline

Answer:

Find $f(3)$ : Use the initial conditions to find $f(3)$ . The recursive formula is $f(n) = f(n-1) - f(n-2)$ . We know $f(1) = 2$ and $f(2) = 1$ . So, $f(3) = f(2) - f(1) = 1 - 2 = -1$ .
Find $f(4)$ : Use the recursive formula to find $f(4)$ . $\newline$ Now we have $f(2) = 1$ and $f(3) = -1$ . $\newline$ So, $f(4) = f(3) - f(2) = -1 - 1 = -2$ .
Find $f(5)$ : Use the recursive formula to find $f(5)$ . $\newline$ Now we have $f(3) = -1$ and $f(4) = -2$ . $\newline$ So, $f(5) = f(4) - f(3) = -2 - (-1) = -2 + 1 = -1$ .