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

Given initial condition and formula: We are given the initial condition and the recursive formula: f(1) = 4 f(n+1) = f(n)^(2) + 4 We need to find f(3). To do this, we will first find f(2) using the given recursive formula. Substitute n=1 into the recursive formula to find f(2). f(2) = f(1)^(2) + 4Calculate f(2): Now we calculate f(2) using the value of f(1). f(2) = 4^(2) + 4 f(2) = 16 + 4 f(2) = 20 We have found f(2) without any mathematical errors.Use f(2) to find f(3): Next, we use the value of f(2) to find f(3) using the recursive formula again. Substitute n=2 into the recursive formula to find f(3). f(3) = f(2)^(2) + 4Calculate f(3): Now we calculate f(3) using the value of f(2). f(3) = 20^(2) + 4 f(3) = 400 + 4 f(3) = 404 We have found f(3) without any mathematical errors.

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Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=4

and

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

then find the value of

f(3)

\newline

Answer:

Given initial condition and formula: We are given the initial condition and the recursive formula: $\newline$ $f(1) = 4$ $\newline$ $f(n+1) = f(n)^{2} + 4$ $\newline$ We need to find $f(3)$ . To do this, we will first find $f(2)$ using the given recursive formula. $\newline$ Substitute $n=1$ into the recursive formula to find $f(2)$ . $\newline$ $f(2) = f(1)^{2} + 4$
Calculate $f(2)$ : Now we calculate $f(2)$ using the value of $f(1)$ .
$f(2) = 4^{2} + 4$
$f(2) = 16 + 4$
$f(2) = 20$
We have found $f(2)$ without any mathematical errors.
Use $f(2)$ to find $f(3)$ : Next, we use the value of $f(2)$ to find $f(3)$ using the recursive formula again. $\newline$ Substitute $n=2$ into the recursive formula to find $f(3)$ . $\newline$ $f(3) = f(2)^{2} + 4$
Calculate $f(3)$ : Now we calculate $f(3)$ using the value of $f(2)$ .
$f(3) = 20^{2} + 4$
$f(3) = 400 + 4$
$f(3) = 404$
We have found $f(3)$ without any mathematical errors.