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

Given initial condition: We are given the initial condition and the recursive formula for the function f: f(1) = 2 f(n+1) = f(n)^(2) + 5 We need to find the value of f(4). We will start by finding f(2) using the given recursive formula. Substitute n=1 into the recursive formula to find f(2). f(2) = f(1)^(2) + 5 f(2) = 2^(2) + 5 f(2) = 4 + 5 f(2) = 9Find f(2): Now that we have f(2), we will use it to find f(3). Substitute n=2 into the recursive formula to find f(3). f(3) = f(2)^(2) + 5 f(3) = 9^(2) + 5 f(3) = 81 + 5 f(3) = 86Find f(3): With f(3) found, we can now find f(4). Substitute n=3 into the recursive formula to find f(4). f(4) = f(3)^(2) + 5 f(4) = 86^(2) + 5 f(4) = 7396 + 5 f(4) = 7401

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

If $f(1)=2$ and $f(n+1)=f(n)^{2}+5$ 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)=2

and

f(n+1)=f(n)^{2}+5

then find the value of

f(4)

\newline

Answer:

Given initial condition: We are given the initial condition and the recursive formula for the function $f$ : $f(1) = 2$ $f(n+1) = f(n)^{2} + 5$ We need to find the value of $f(4)$ . We will start by finding $f(2)$ using the given recursive formula. $\newline$ Substitute $n=1$ into the recursive formula to find $f(2)$ . $f(2) = f(1)^{2} + 5$ $f(2) = 2^{2} + 5$ $f(2) = 4 + 5$ $f(2) = 9$
Find $f(2)$ : Now that we have $f(2)$ , we will use it to find $f(3)$ . $\newline$ Substitute $n=2$ into the recursive formula to find $f(3)$ . $\newline$ $f(3) = f(2)^{2} + 5$ $\newline$ $f(3) = 9^{2} + 5$ $\newline$ $f(3) = 81 + 5$ $\newline$ $f(3) = 86$
Find $f(3)$ : With $f(3)$ found, we can now find $f(4)$ . Substitute $n=3$ into the recursive formula to find $f(4)$ . $f(4) = f(3)^{2} + 5$ $f(4) = 86^{2} + 5$ $f(4) = 7396 + 5$ $f(4) = 7401$