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

Given initial condition: We are given the initial condition f(1) = 2 and the recursive formula f(n) = 4f(n-1) + 1. To find f(5), we need to find the values of f(2), f(3), and f(4) first, using the recursive formula.Find f(2): Using the recursive formula, let's find f(2): f(2) = 4f(2-1) + 1 f(2) = 4f(1) + 1 f(2) = 4(2) + 1 f(2) = 8 + 1 f(2) = 9Find f(3): Now, let's find f(3): f(3) = 4f(3-1) + 1 f(3) = 4f(2) + 1 f(3) = 4(9) + 1 f(3) = 36 + 1 f(3) = 37Find f(4): Next, we find f(4): f(4) = 4f(4-1) + 1 f(4) = 4f(3) + 1 f(4) = 4(37) + 1 f(4) = 148 + 1 f(4) = 149Find f(5): Finally, we can find f(5): f(5) = 4f(5-1) + 1 f(5) = 4f(4) + 1 f(5) = 4(149) + 1 f(5) = 596 + 1 f(5) = 597

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

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

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Q. If

f(1)=2

and

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

then find the value of

f(5)

\newline

Answer:

Given initial condition: We are given the initial condition $f(1) = 2$ and the recursive formula $f(n) = 4f(n-1) + 1$ . To find $f(5)$ , we need to find the values of $f(2)$ , $f(3)$ , and $f(4)$ first, using the recursive formula.
Find $f(2)$ : Using the recursive formula, let's find $f(2)$ :
$f(2) = 4f(2-1) + 1$
$f(2) = 4f(1) + 1$
$f(2) = 4(2) + 1$
$f(2) = 8 + 1$
$f(2) = 9$
Find $f(3)$ : Now, let's find $f(3)$ :
$f(3) = 4f(3-1) + 1$
$f(3) = 4f(2) + 1$
$f(3) = 4(9) + 1$
$f(3) = 36 + 1$
$f(3) = 37$
Find $f(4)$ : Next, we find $f(4)$ :
$f(4) = 4f(4-1) + 1$
$f(4) = 4f(3) + 1$
$f(4) = 4(37) + 1$
$f(4) = 148 + 1$
$f(4) = 149$
Find $f(5)$ : Finally, we can find $f(5)$ :
$f(5) = 4f(5-1) + 1$
$f(5) = 4f(4) + 1$
$f(5) = 4(149) + 1$
$f(5) = 596 + 1$
$f(5) = 597$