If f(1)=10 and f(n)=4f(n-1)+n then find the value of f(4). Answer:

Given f(1) = 10: We are given that f(1) = 10. 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) = 4f(n-1) + n. First, let's find f(2) using the given formula: f(2) = 4f(2-1) + 2 f(2) = 4f(1) + 2 f(2) = 4(10) + 2 f(2) = 40 + 2 f(2) = 42Find f(2): Now that we have f(2), we can find f(3): f(3) = 4f(3-1) + 3 f(3) = 4f(2) + 3 f(3) = 4(42) + 3 f(3) = 168 + 3 f(3) = 171Find f(3): Finally, we can find f(4) using the value of f(3): f(4) = 4f(4-1) + 4 f(4) = 4f(3) + 4 f(4) = 4(171) + 4 f(4) = 684 + 4 f(4) = 688

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If
f(1)=10 and
f(n)=4f(n-1)+n then find the value of
f(4).
Answer:

If $f(1)=10$ and $f(n)=4 f(n-1)+n$ then find the value of $f(4)$ . $\newline$ Answer:

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Full solution

Q. If

f(1)=10

and

f(n)=4 f(n-1)+n

then find the value of

f(4)

\newline

Answer:

Given $f(1) = 10$ : We are given that $f(1) = 10$ . To find $f(4)$ , we need to find the values of $f(2)$ , $f(3)$ , and then $f(4)$ using the recursive formula $f(n) = 4f(n-1) + n$ . First, let's find $f(2)$ using the given formula: $f(2) = 4f(2-1) + 2$ $f(2) = 4f(1) + 2$ $f(1) = 10$ $0$ $f(1) = 10$ $1$ $f(1) = 10$ $2$
Find $f(2)$ : Now that we have $f(2)$ , we can find $f(3)$ :
$f(3) = 4f(3-1) + 3$
$f(3) = 4f(2) + 3$
$f(3) = 4(42) + 3$
$f(3) = 168 + 3$
$f(3) = 171$
Find $f(3)$ : Finally, we can find $f(4)$ using the value of $f(3)$ :
$f(4) = 4f(4-1) + 4$
$f(4) = 4f(3) + 4$
$f(4) = 4(171) + 4$
$f(4) = 684 + 4$
$f(4) = 688$