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

If $a_{1}=3$ 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}=3

and

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

then find the value of

a_{4}

.

\newline

Answer:

Given sequence: Given the recursive sequence: $\newline$ $a_1 = 3$ $\newline$ $a_{n+1} = a_n^2 + 2$ $\newline$ We need to find the value of $a_4$ . $\newline$ First, let's find $a_2$ using the given formula. $\newline$ $a_2 = a_1^2 + 2$
Calculate $a_{2}$ : Now we calculate $a_{2}$ using the value of $a_{1}$ which is $3$ . $\newline$ $a_{2} = (3)^2 + 2$ $\newline$ $a_{2} = 9 + 2$ $\newline$ $a_{2} = 11$
Find $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ .
$a_{3} = (a_{2})^2 + 2$
$a_{3} = (11)^2 + 2$
Calculate $a_{3}$ : We calculate $a_{3}$ using the value of $a_{2}$ which is $11$ . $\newline$ $a_{3} = 121 + 2$ $\newline$ $a_{3} = 123$
Find $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ .
$a_{4} = (a_{3})^2 + 2$
$a_{4} = (123)^2 + 2$
Calculate $a_{4}$ : We calculate $a_{4}$ using the value of $a_{3}$ which is $123$ . $\newline$ $a_{4} = 15129 + 2$ $\newline$ $a_{4} = 15131$

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