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

Calculate a_(2): Determine the value of a_(2) using the given recursive formula. The recursive formula is a_(n+1)=(a_(n))^2+2. We know that a_(1)=3, so we can find a_(2) by plugging n=1 into the formula. a_(2) = (a_(1))^2 + 2 = 3^2 + 2 = 9 + 2 = 11.Calculate a_(3): Determine the value of a_(3) using the recursive formula and the value of a_(2). Now that we have a_(2)=11, we can find a_(3) by plugging n=2 into the formula. a_(3) = (a_(2))^2 + 2 = 11^2 + 2 = 121 + 2 = 123.

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

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

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Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=3

and

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

then find the value of

a_{3}

\newline

Answer:

Calculate $a_{2}$ : Determine the value of $a_{2}$ using the given recursive formula. $\newline$ The recursive formula is $a_{n+1}=(a_{n})^2+2$ . We know that $a_{1}=3$ , so we can find $a_{2}$ by plugging $n=1$ into the formula. $\newline$ $a_{2} = (a_{1})^2 + 2 = 3^2 + 2 = 9 + 2 = 11$ .
Calculate $a_{3}$ : Determine the value of $a_{3}$ using the recursive formula and the value of $a_{2}$ . $\newline$ Now that we have $a_{2}=11$ , we can find $a_{3}$ by plugging $n=2$ into the formula. $\newline$ $a_{3} = (a_{2})^2 + 2 = 11^2 + 2 = 121 + 2 = 123$ .