If f(1)=4 and f(n)=nf(n-1)-2 then find the value of f(5). Answer:

Given Information: We are given that f(1) = 4. To find f(5), we need to use the recursive formula f(n) = nf(n-1) - 2, starting with n = 2 and working our way up to n = 5.Calculate f(2): First, let's find f(2) using the formula: f(2) = 2f(2-1) - 2 f(2) = 2f(1) - 2 f(2) = 2(4) - 2 f(2) = 8 - 2 f(2) = 6Calculate f(3): Next, we find f(3) using the value of f(2) we just calculated: f(3) = 3f(3-1) - 2 f(3) = 3f(2) - 2 f(3) = 3(6) - 2 f(3) = 18 - 2 f(3) = 16Calculate f(4): Now, we calculate f(4) using the value of f(3): f(4) = 4f(4-1) - 2 f(4) = 4f(3) - 2 f(4) = 4(16) - 2 f(4) = 64 - 2 f(4) = 62Calculate f(5): Finally, we find f(5) using the value of f(4): f(5) = 5f(5-1) - 2 f(5) = 5f(4) - 2 f(5) = 5(62) - 2 f(5) = 310 - 2 f(5) = 308

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If
f(1)=4 and
f(n)=nf(n-1)-2 then find the value of
f(5).
Answer:

If $f(1)=4$ and $f(n)=n f(n-1)-2$ then find the value of $f(5)$ . $\newline$ Answer:

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Full solution

Q. If

f(1)=4

and

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

then find the value of

f(5)

\newline

Answer:

Given Information: We are given that $f(1) = 4$ . To find $f(5)$ , we need to use the recursive formula $f(n) = nf(n-1) - 2$ , starting with $n = 2$ and working our way up to $n = 5$ .
Calculate $f(2)$ : First, let's find $f(2)$ using the formula: $\newline$ $f(2) = 2f(2-1) - 2$ $\newline$ $f(2) = 2f(1) - 2$ $\newline$ $f(2) = 2(4) - 2$ $\newline$ $f(2) = 8 - 2$ $\newline$ $f(2) = 6$
Calculate $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ we just calculated: $\newline$ $f(3) = 3f(3-1) - 2$ $\newline$ $f(3) = 3f(2) - 2$ $\newline$ $f(3) = 3(6) - 2$ $\newline$ $f(3) = 18 - 2$ $\newline$ $f(3) = 16$
Calculate $f(4)$ : Now, we calculate $f(4)$ using the value of $f(3)$ :
$f(4) = 4f(4-1) - 2$
$f(4) = 4f(3) - 2$
$f(4) = 4(16) - 2$
$f(4) = 64 - 2$
$f(4) = 62$
Calculate $f(5)$ : Finally, we find $f(5)$ using the value of $f(4)$ :
$f(5) = 5f(5-1) - 2$
$f(5) = 5f(4) - 2$
$f(5) = 5(62) - 2$
$f(5) = 310 - 2$
$f(5) = 308$