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

Given initial condition: We are given the initial condition f(1) = 3 and the recursive formula f(n) = f(n-1)^(2) + 4. To find f(4), we first need to find f(2), f(3), and then f(4) using the recursive formula.Find f(2): Using the recursive formula, let's find f(2): f(2) = f(1)^(2) + 4 Substitute the value of f(1) into the equation: f(2) = 3^(2) + 4 f(2) = 9 + 4 f(2) = 13Find f(3): Next, we find f(3) using the value of f(2): f(3) = f(2)^(2) + 4 Substitute the value of f(2) into the equation: f(3) = 13^(2) + 4 f(3) = 169 + 4 f(3) = 173Find f(4): Finally, we find f(4) using the value of f(3): f(4) = f(3)^(2) + 4 Substitute the value of f(3) into the equation: f(4) = 173^(2) + 4 f(4) = 29929 + 4 f(4) = 29933

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

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

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Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=3

and

f(n)=f(n-1)^{2}+4

then find the value of

f(4)

\newline

Answer:

Given initial condition: We are given the initial condition $f(1) = 3$ and the recursive formula $f(n) = f(n-1)^{2} + 4$ . To find $f(4)$ , we first need to find $f(2)$ , $f(3)$ , and then $f(4)$ using the recursive formula.
Find $f(2)$ : Using the recursive formula, let's find $f(2)$ :
$f(2) = f(1)^{2} + 4$
Substitute the value of $f(1)$ into the equation:
$f(2) = 3^{2} + 4$
$f(2) = 9 + 4$
$f(2) = 13$
Find $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ :
$f(3) = f(2)^{2} + 4$
Substitute the value of $f(2)$ into the equation:
$f(3) = 13^{2} + 4$
$f(3) = 169 + 4$
$f(3) = 173$
Find $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ :
$f(4) = f(3)^{2} + 4$
Substitute the value of $f(3)$ into the equation:
$f(4) = 173^{2} + 4$
$f(4) = 29929 + 4$
$f(4) = 29933$