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

Given conditions: We are given the initial condition and the recursive formula: f(1) = 1 f(n+1) = f(n)^(2) + 5 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) + 5 f(2) = 1^2 + 5 f(2) = 1 + 5 f(2) = 6Find f(2): Now that we have f(2), let's find f(3) using the recursive formula. Substitute n = 2 into the recursive formula to find f(3). f(3) = f(2)^(2) + 5 f(3) = 6^2 + 5 f(3) = 36 + 5 f(3) = 41Find f(3): Finally, we will find f(4) using the recursive formula. Substitute n = 3 into the recursive formula to find f(4). f(4) = f(3)^(2) + 5 f(4) = 41^2 + 5 f(4) = 1681 + 5 f(4) = 1686

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. If

f(1)=1

and

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

then find the value of

f(4)

\newline

Answer:

Given conditions: We are given the initial condition and the recursive formula: $\newline$ $f(1) = 1$ $\newline$ $f(n+1) = f(n)^{2} + 5$ $\newline$ 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 $f(2)$ . $\newline$ $f(2) = f(1)^{2} + 5$ $\newline$ $f(2) = 1^2 + 5$ $\newline$ $f(2) = 1 + 5$ $\newline$ $f(2) = 6$
Find $f(2)$ : Now that we have $f(2)$ , let's find $f(3)$ using the recursive formula. $\newline$ Substitute $n = 2$ into the recursive formula to find $f(3)$ . $\newline$ $f(3) = f(2)^{2} + 5$ $\newline$ $f(3) = 6^{2} + 5$ $\newline$ $f(3) = 36 + 5$ $\newline$ $f(3) = 41$
Find $f(3)$ : Finally, we will find $f(4)$ using the recursive formula. $\newline$ Substitute $n = 3$ into the recursive formula to find $f(4)$ . $\newline$ $f(4) = f(3)^{2} + 5$ $\newline$ $f(4) = 41^{2} + 5$ $\newline$ $f(4) = 1681 + 5$ $\newline$ $f(4) = 1686$