If f(1)=2 and f(n)=-3f(n-1)+n then find the value of f(4). Answer:

Given f(1): We are given that f(1) = 2. To find f(4), we need to find the values of f(2), f(3), and then f(4) using the recursive formula f(n) = -3f(n-1) + n.Find f(2): First, let's find f(2) using the formula: f(2) = -3f(2-1) + 2 f(2) = -3f(1) + 2 f(2) = -3(2) + 2 f(2) = -6 + 2 f(2) = -4Find f(3): Next, we find f(3) using the formula and the value of f(2) we just found: f(3) = -3f(3-1) + 3 f(3) = -3f(2) + 3 f(3) = -3(-4) + 3 f(3) = 12 + 3 f(3) = 15Find f(4): Finally, we find f(4) using the formula and the value of f(3): f(4) = -3f(4-1) + 4 f(4) = -3f(3) + 4 f(4) = -3(15) + 4 f(4) = -45 + 4 f(4) = -41

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If
f(1)=2 and
f(n)=-3f(n-1)+n then find the value of
f(4).
Answer:

If $f(1)=2$ and $f(n)=-3 f(n-1)+n$ then find the value of $f(4)$ . $\newline$ Answer:

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Q. If

f(1)=2

and

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

then find the value of

f(4)

\newline

Answer:

Given $f(1)$ : We are given that $f(1) = 2$ . To find $f(4)$ , we need to find the values of $f(2)$ , $f(3)$ , and then $f(4)$ using the recursive formula $f(n) = -3f(n-1) + n$ .
Find $f(2)$ : First, let's find $f(2)$ using the formula: $\newline$ $f(2) = -3f(2-1) + 2$ $\newline$ $f(2) = -3f(1) + 2$ $\newline$ $f(2) = -3(2) + 2$ $\newline$ $f(2) = -6 + 2$ $\newline$ $f(2) = -4$
Find $f(3)$ : Next, we find $f(3)$ using the formula and the value of $f(2)$ we just found: $\newline$ $f(3) = -3f(3-1) + 3$ $\newline$ $f(3) = -3f(2) + 3$ $\newline$ $f(3) = -3(-4) + 3$ $\newline$ $f(3) = 12 + 3$ $\newline$ $f(3) = 15$
Find $f(4)$ : Finally, we find $f(4)$ using the formula and the value of $f(3)$ :
$f(4) = -3f(4-1) + 4$
$f(4) = -3f(3) + 4$
$f(4) = -3(15) + 4$
$f(4) = -45 + 4$
$f(4) = -41$