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

Given terms and formula: We are given the first term of the sequence, a_(1) = 2, and the recursive formula for the sequence, a_(n+1) = (a_(n))^2 - 4. 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 a_(1): a_(2) = (a_(1))^2 - 4 a_(2) = (2)^2 - 4 a_(2) = 4 - 4 a_(2) = 0Find a_(3): Next, we find a_(3) using the recursive formula and the value of a_(2) we just found: a_(3) = (a_(2))^2 - 4 a_(3) = (0)^2 - 4 a_(3) = 0 - 4 a_(3) = -4Find a_(4): Finally, we find a_(4) using the recursive formula and the value of a_(3): a_(4) = (a_(3))^2 - 4 a_(4) = (-4)^2 - 4 a_(4) = 16 - 4 a_(4) = 12

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

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

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Algebra 2

Transformations of functions

Full solution

Q. If

a_{1}=2

and

a_{n+1}=\left(a_{n}\right)^{2}-4

then find the value of

a_{4}

\newline

Answer:

Given terms and formula: We are given the first term of the sequence, $a_{1} = 2$ , and the recursive formula for the sequence, $a_{n+1} = (a_{n})^2 - 4$ . 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 $a_{1}$ : $a_{2} = (a_{1})^2 - 4$ $a_{2} = (2)^2 - 4$ $a_{2} = 4 - 4$ $a_{2} = 0$
Find $a_{3}$ : Next, we find $a_{3}$ using the recursive formula and the value of $a_{2}$ we just found: $\newline$ $a_{3} = (a_{2})^2 - 4$ $\newline$ $a_{3} = (0)^2 - 4$ $\newline$ $a_{3} = 0 - 4$ $\newline$ $a_{3} = -4$
Find $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula and the value of $a_{3}$ : $a_{4} = (a_{3})^2 - 4$ $a_{4} = (-4)^2 - 4$ $a_{4} = 16 - 4$ $a_{4} = 12$