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

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

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Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=1

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 for the function $f$ : $f(1) = 1$ $f(n+1) = f(n)^{2} + 4$ To find $f(3)$ , we first need to find $f(2)$ using the recursive formula.Substitute $n=1$ into the recursive formula to find $f(2)$ . $f(2) = f(1)^{2} + 4$ $f(2) = 1^2 + 4$ $f(2) = 1 + 4$ $f(1) = 1$ $0$
Find $f(2)$ : Now that we have $f(2)$ , we can find $f(3)$ using the recursive formula again. $\newline$ Substitute $n=2$ into the recursive formula to find $f(3)$ . $\newline$ $f(3) = f(2)^{2} + 4$ $\newline$ $f(3) = 5^2 + 4$ $\newline$ $f(3) = 25 + 4$ $\newline$ $f(3) = 29$

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