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

If $a_{1}=4$ and $a_{n}=\left(a_{n-1}\right)^{2}+n$ 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}=4

and

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

then find the value of

a_{4}

.

\newline

Answer:

Find $a_{2}$ : Given $a_{1} = 4$ , we need to find $a_{4}$ using the recursive formula $a_{n} = (a_{n-1})^2 + n$ . We will start by finding $a_{2}$ . $\newline$ $a_{2} = (a_{1})^2 + 2$ $\newline$ $\quad = (4)^2 + 2$ $\newline$ $\quad = 16 + 2$ $\newline$ $\quad = 18$
Find $a_{3}$ : Now we will find $a_{3}$ using $a_{2}$ . $\newline$ $a_{3} = (a_{2})^2 + 3 = (18)^2 + 3 = 324 + 3 = 327$
Find $a_{4}$ : Finally, we will find $a_{4}$ using $a_{3}$ . $\newline$ $a_{4} = (a_{3})^2 + 4 = (327)^2 + 4 = 106929 + 4 = 106933$

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