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

Given Information: We are given the first term of the sequence, a_(1)=2, and the recursive formula for the sequence, a_(n)=(a_(n-1))^(2)+1. To find a_(4), we need to find the values of 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): a_(2) = (a_(1))^(2) + 1 a_(2) = (2)^(2) + 1 a_(2) = 4 + 1 a_(2) = 5Find a_(3): Next, we find a_(3) using the value of a_(2): a_(3) = (a_(2))^(2) + 1 a_(3) = (5)^(2) + 1 a_(3) = 25 + 1 a_(3) = 26Find a_(4): Finally, we find a_(4) using the value of a_(3): a_(4) = (a_(3))^(2) + 1 a_(4) = (26)^(2) + 1 a_(4) = 676 + 1 a_(4) = 677

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

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

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Math Problems

Algebra 2

Transformations of functions

Full solution

Q. If

a_{1}=2

and

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

then find the value of

a_{4}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=2$ , and the recursive formula for the sequence, $a_{n}=(a_{n-1})^{2}+1$ . To find $a_{4}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula and the given $a_{1}$ : $a_{2} = (a_{1})^{2} + 1$ $a_{2} = (2)^{2} + 1$ $a_{2} = 4 + 1$ $a_{2} = 5$
Find $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ :
$a_{3} = (a_{2})^{2} + 1$
$a_{3} = (5)^{2} + 1$
$a_{3} = 25 + 1$
$a_{3} = 26$
Find $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ :
$a_{4} = (a_{3})^{2} + 1$
$a_{4} = (26)^{2} + 1$
$a_{4} = 676 + 1$
$a_{4} = 677$