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

Given Information: We are given the first term of the sequence, a_(1)=4, and the recursive formula for the sequence, a_(n)=(a_(n-1))^2+3. To find a_(3), we first need to find a_(2).Finding a_(2): Using the recursive formula, we substitute n=2 to find a_(2): a_(2) = (a_(2-1))^2 + 3 a_(2) = (a_(1))^2 + 3 a_(2) = 4^2 + 3 a_(2) = 16 + 3 a_(2) = 19 We have found that a_(2) is 19.Finding a_(3): Now we use the value of a_(2) to find a_(3) using the same recursive formula: a_(3) = (a_(3-1))^2 + 3 a_(3) = (a_(2))^2 + 3 a_(3) = 19^2 + 3 a_(3) = 361 + 3 a_(3) = 364 We have found that a_(3) is 364.

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

If $a_{1}=4$ 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}=4

and

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

then find the value of

a_{3}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=4$ , and the recursive formula for the sequence, $a_{n}=(a_{n-1})^2+3$ . To find $a_{3}$ , we first need to find $a_{2}$ .
Finding $a_{2}$ : Using the recursive formula, we substitute $n=2$ to find $a_{2}$ :
$a_{2} = (a_{2-1})^2 + 3$
$a_{2} = (a_{1})^2 + 3$
$a_{2} = 4^2 + 3$
$a_{2} = 16 + 3$
$a_{2} = 19$
We have found that $a_{2}$ is $19$ .
Finding $a_{3}$ : Now we use the value of $a_{2}$ to find $a_{3}$ using the same recursive formula: $\newline$ $a_{3} = (a_{3-1})^2 + 3$ $\newline$ $a_{3} = (a_{2})^2 + 3$ $\newline$ $a_{3} = 19^2 + 3$ $\newline$ $a_{3} = 361 + 3$ $\newline$ $a_{3} = 364$ $\newline$ We have found that $a_{3}$ is $364$ .