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

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

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Transformations of functions

Full solution

Q. If

a_{1}=2

and

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

then find the value of

a_{4}

.

\newline

Answer:

Find $a_{2}$ : Use the given recursive formula to find $a_{2}$ . The recursive formula is $a_{n+1} = (a_{n})^2 - 2$ . We know that $a_{1} = 2$ . Calculate $a_{2}$ using $a_{1}$ : $a_{2} = (a_{1})^2 - 2 = (2)^2 - 2 = 4 - 2$ .
Find $a_{3}$ : Use the recursive formula to find $a_{3}$ . Now that we have $a_{2}$ , we can find $a_{3}$ using the same formula: $a_{3} = (a_{2})^2 - 2 = (4)^2 - 2 = 16 - 2$ .
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ . With $a_{3}$ found, we can calculate $a_{4}$ : $a_{4} = (a_{3})^2 - 2 = (16)^2 - 2 = 256 - 2$ .

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