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

Given information: We are given the first term of the sequence, a_(1)=4, and the recursive formula for the sequence, a_(n+1)=(a_(n))^2+3. To find a_(4), we need to find a_(2), a_(3), and then a_(4) using the recursive formula.Find a_(2): First, let's find a_(2) using the recursive formula and the given a_(1)=4. a_(2) = (a_(1))^2 + 3 = 4^2 + 3 = 16 + 3 = 19.Find a_(3): Next, we find a_(3) using the value of a_(2) we just found. a_(3) = (a_(2))^2 + 3 = 19^2 + 3 = 361 + 3 = 364.Find a_(4): Finally, we find a_(4) using the value of a_(3). a_(4) = (a_(3))^2 + 3 = 364^2 + 3 = 132,496 + 3 = 132,499.

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

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

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Precalculus

Find the roots of factored polynomials

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Q. If

a_{1}=4

and

a_{n+1}=\left(a_{n}\right)^{2}+3

then find the value of

a_{4}

\newline

Answer:

Given information: We are given the first term of the sequence, $a_{1}=4$ , and the recursive formula for the sequence, $a_{n+1}=(a_{n})^2+3$ . To find $a_{4}$ , we need to find $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula and the given $a_{1}=4$ . $\newline$ $a_{2} = (a_{1})^2 + 3 = 4^2 + 3 = 16 + 3 = 19$ .
Find $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ we just found. $\newline$ $a_{3} = (a_{2})^2 + 3 = 19^2 + 3 = 361 + 3 = 364$ .
Find $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ . $\newline$ $a_{4} = (a_{3})^2 + 3 = 364^2 + 3 = 132,496 + 3 = 132,499$ .