If a_(1)=4 and a_(n+1)=(a_(n))^(2)-5 then find the value of a_(4). Answer:

Given terms: 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 - 5. 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 first term a_(1) = 4. a_(2) = (a_(1))^2 - 5 = 4^2 - 5 = 16 - 5 = 11.Find a_(3): Next, we find a_(3) using the value of a_(2) we just found. a_(3) = (a_(2))^2 - 5 = 11^2 - 5 = 121 - 5 = 116.Find a_(4): Finally, we find a_(4) using the value of a_(3). a_(4) = (a_(3))^2 - 5 = 116^2 - 5 = 13456 - 5 = 13451.

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If
a_(1)=4 and
a_(n+1)=(a_(n))^(2)-5 then find the value of
a_(4).
Answer:

If $a_{1}=4$ and $a_{n+1}=\left(a_{n}\right)^{2}-5$ then find the value of $a_{4}$ . $\newline$ Answer:

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Algebra 2

Transformations of functions

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Q. If

a_{1}=4

and

a_{n+1}=\left(a_{n}\right)^{2}-5

then find the value of

a_{4}

\newline

Answer:

Given terms: We are given the first term of the sequence, $a_{1} = 4$ , and the recursive formula for the sequence, $a_{n+1} = (a_{n})^2 - 5$ . 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 first term $a_{1} = 4$ . $\newline$ $a_{2} = (a_{1})^2 - 5 = 4^2 - 5 = 16 - 5 = 11$ .
Find $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ we just found. $\newline$ $a_{3} = (a_{2})^2 - 5 = 11^2 - 5 = 121 - 5 = 116$ .
Find $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ . $\newline$ $a_{$4$} = (a_{$3$})^$2$ - $5$ = $116$^$2$ - $5$ = $13456$ - $5$ = $13451$.