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

Given Initial Condition and Formula: We are given the initial condition and the recursive formula: f(1) = 2 f(n+1) = f(n)^(2) + 4 We need to find f(4). Let's start by finding 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) = 2^(2) + 4 f(2) = 4 + 4 f(2) = 8Find f(2): Now that we have f(2), we can find f(3) using the recursive formula. Substitute n=2 into the recursive formula to find f(3). f(3) = f(2)^(2) + 4 f(3) = 8^(2) + 4 f(3) = 64 + 4 f(3) = 68Find f(3): Finally, we can find f(4) using the recursive formula. Substitute n=3 into the recursive formula to find f(4). f(4) = f(3)^(2) + 4 f(4) = 68^(2) + 4 f(4) = 4624 + 4 f(4) = 4628

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Math Problems

Algebra 2

Evaluate expression when two complex numbers are given

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Q. If

f(1)=2

and

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

then find the value of

f(4)

\newline

Answer:

Given Initial Condition and Formula: We are given the initial condition and the recursive formula: $\newline$ $f(1) = 2$ $\newline$ $f(n+1) = f(n)^{2} + 4$ $\newline$ We need to find $f(4)$ . Let's start by finding $f(2)$ using the recursive formula. $\newline$ Substitute $n=1$ into the recursive formula to find $f(2)$ . $\newline$ $f(2) = f(1)^{2} + 4$ $\newline$ $f(2) = 2^{2} + 4$ $\newline$ $f(2) = 4 + 4$ $\newline$ $f(2) = 8$
Find $f(2)$ : Now that we have $f(2)$ , we can find $f(3)$ using the recursive formula. $\newline$ Substitute $n=2$ into the recursive formula to find $f(3)$ . $\newline$ $f(3) = f(2)^{2} + 4$ $\newline$ $f(3) = 8^{2} + 4$ $\newline$ $f(3) = 64 + 4$ $\newline$ $f(3) = 68$
Find $f(3)$ : Finally, we can find $f(4)$ using the recursive formula. $\newline$ Substitute $n=3$ into the recursive formula to find $f(4)$ . $\newline$ $f(4) = f(3)^{2} + 4$ $\newline$ $f(4) = 68^{2} + 4$ $\newline$ $f(4) = 4624 + 4$ $\newline$ $f(4) = 4628$