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

Given f(1) = 1: We are given that f(1) = 1. To find f(5), we need to apply the recursive formula f(n) = -3f(n-1) + 3 for each subsequent value of n until we reach n = 5.Find f(2): First, let's find f(2) using the formula with n = 2. f(2) = -3f(2-1) + 3 f(2) = -3f(1) + 3 Since we know f(1) = 1, we can substitute it in: f(2) = -3(1) + 3 f(2) = -3 + 3 f(2) = 0Find f(3): Next, we find f(3) using the formula with n = 3. f(3) = -3f(3-1) + 3 f(3) = -3f(2) + 3 We have already found f(2) = 0, so we substitute it in: f(3) = -3(0) + 3 f(3) = 0 + 3 f(3) = 3Find f(4): Now, we find f(4) using the formula with n = 4. f(4) = -3f(4-1) + 3 f(4) = -3f(3) + 3 We have already found f(3) = 3, so we substitute it in: f(4) = -3(3) + 3 f(4) = -9 + 3 f(4) = -6Find f(5): Finally, we find f(5) using the formula with n = 5. f(5) = -3f(5-1) + 3 f(5) = -3f(4) + 3 We have already found f(4) = -6, so we substitute it in: f(5) = -3(-6) + 3 f(5) = 18 + 3 f(5) = 21

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

If $f(1)=1$ and $f(n)=-3 f(n-1)+3$ then find the value of $f(5)$ . $\newline$ Answer:

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Full solution

Q. If

f(1)=1

and

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

then find the value of

f(5)

\newline

Answer:

Given $f(1) = 1$ : We are given that $f(1) = 1$ . To find $f(5)$ , we need to apply the recursive formula $f(n) = -3f(n-1) + 3$ for each subsequent value of $n$ until we reach $n = 5$ .
Find $f(2)$ : First, let's find $f(2)$ using the formula with $n = 2$ .
$f(2) = -3f(2-1) + 3$
$f(2) = -3f(1) + 3$
Since we know $f(1) = 1$ , we can substitute it in:
$f(2) = -3(1) + 3$
$f(2) = -3 + 3$
$f(2) = 0$
Find $f(3)$ : Next, we find $f(3)$ using the formula with $n = 3$ .
$f(3) = -3f(3-1) + 3$
$f(3) = -3f(2) + 3$
We have already found $f(2) = 0$ , so we substitute it in:
$f(3) = -3(0) + 3$
$f(3) = 0 + 3$
$f(3) = 3$
Find $f(4)$ : Now, we find $f(4)$ using the formula with $n = 4$ .
$f(4) = -3f(4-1) + 3$
$f(4) = -3f(3) + 3$
We have already found $f(3) = 3$ , so we substitute it in:
$f(4) = -3(3) + 3$
$f(4) = -9 + 3$
$f(4) = -6$
Find $f(5)$ : Finally, we find $f(5)$ using the formula with $n = 5$ .
$f(5) = -3f(5-1) + 3$
$f(5) = -3f(4) + 3$
We have already found $f(4) = -6$ , so we substitute it in:
$f(5) = -3(-6) + 3$
$f(5) = 18 + 3$
$f(5) = 21$