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

Find a_(2) Value: Determine the value of a_(2) using the recursive formula. We know that a_(1) = 1. To find a_(2), we use the formula a_(n) = (a_(n-1))^2 + 3 with n=2. a_(2) = (a_(2-1))^2 + 3 a_(2) = (a_(1))^2 + 3 a_(2) = (1)^2 + 3 a_(2) = 1 + 3 a_(2) = 4Calculate a_(3) Value: Determine the value of a_(3) using the recursive formula. Now that we have a_(2) = 4, we can find a_(3) using the same formula. a_(3) = (a_(3-1))^2 + 3 a_(3) = (a_(2))^2 + 3 a_(3) = (4)^2 + 3 a_(3) = 16 + 3 a_(3) = 19

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

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

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. If

a_{1}=1

and

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

then find the value of

a_{3}

\newline

Answer:

Find $a_{2}$ Value: Determine the value of $a_{2}$ using the recursive formula. $\newline$ We know that $a_{1} = 1$ . To find $a_{2}$ , we use the formula $a_{n} = (a_{n-1})^2 + 3$ with $n=2$ . $\newline$ $a_{2} = (a_{2-1})^2 + 3$ $\newline$ $a_{2} = (a_{1})^2 + 3$ $\newline$ $a_{2} = (1)^2 + 3$ $\newline$ $a_{2} = 1 + 3$ $\newline$ $a_{2}$ $0$
Calculate $a_{3}$ Value: Determine the value of $a_{3}$ using the recursive formula. $\newline$ Now that we have $a_{2} = 4$ , we can find $a_{3}$ using the same formula. $\newline$ $a_{3} = (a_{3-1})^2 + 3$ $\newline$ $a_{3} = (a_{2})^2 + 3$ $\newline$ $a_{3} = (4)^2 + 3$ $\newline$ $a_{3} = 16 + 3$ $\newline$ $a_{3} = 19$