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

Given initial condition: We are given the initial condition f(1) = 3 and the recursive formula f(n) = f(n-1)^(2) + 2. To find f(4), we need to first find f(2), then f(3), and finally f(4) using the recursive formula.Find f(2): Using the recursive formula, let's find f(2): f(2) = f(1)^(2) + 2 Substitute the value of f(1) into the equation: f(2) = 3^(2) + 2 f(2) = 9 + 2 f(2) = 11Find f(3): Now, let's find f(3) using the value of f(2): f(3) = f(2)^(2) + 2 Substitute the value of f(2) into the equation: f(3) = 11^(2) + 2 f(3) = 121 + 2 f(3) = 123Find f(4): Finally, we can find f(4) using the value of f(3): f(4) = f(3)^(2) + 2 Substitute the value of f(3) into the equation: f(4) = 123^(2) + 2 f(4) = 15129 + 2 f(4) = 15131

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

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

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Math Problems

Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=3

and

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

then find the value of

f(4)

\newline

Answer:

Given initial condition: We are given the initial condition $f(1) = 3$ and the recursive formula $f(n) = f(n-1)^{2} + 2$ . To find $f(4)$ , we need to first find $f(2)$ , then $f(3)$ , and finally $f(4)$ using the recursive formula.
Find $f(2)$ : Using the recursive formula, let's find $f(2)$ :
$f(2) = f(1)^{2} + 2$
Substitute the value of $f(1)$ into the equation:
$f(2) = 3^{2} + 2$
$f(2) = 9 + 2$
$f(2) = 11$
Find $f(3)$ : Now, let's find $f(3)$ using the value of $f(2)$ :
$f(3) = f(2)^{2} + 2$
Substitute the value of $f(2)$ into the equation:
$f(3) = 11^{2} + 2$
$f(3) = 121 + 2$
$f(3) = 123$
Find $f(4)$ : Finally, we can find $f(4)$ using the value of $f(3)$ :
$f(4) = f(3)^{2} + 2$
Substitute the value of $f(3)$ into the equation:
$f(4) = 123^{2} + 2$
$f(4) = 15129 + 2$
$f(4) = 15131$