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

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

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. If

a_{1}=2

and

a_{n+1}=\left(a_{n}\right)^{2}+2

then find the value of

a_{4}

.

\newline

Answer:

Calculate $a_{2}$ : Given the recursive sequence where $a_{1}=2$ and $a_{n+1}=(a_{n})^2+2$ , we need to find the value of $a_{4}$ . We start by finding $a_{2}$ using the given formula. $\newline$ a_{2} = (a_{1})^2 + 2\(\newline = (2)^2 + 2 $\newline$ = 4 + 2 $\newline$ = 6\)
Calculate $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ we just found. $\newline$ a_{3} = (a_{2})^2 + 2\(\newline = (6)^2 + 2 $\newline$ = 36 + 2 $\newline$ = 38\)
Calculate $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ . $\newline$ $a_{4} = (a_{3})^2 + 2 = (38)^2 + 2 = 1444 + 2 = 1446$

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