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

Calculate a_(2): We are given that a_(1) = 4. To find a_(3), we first need to find a_(2) using the recursive formula a_(n) = (a_(n-1))^2 - 1. Calculate a_(2) using a_(1): a_(2) = (a_(1))^2 - 1 a_(2) = (4)^2 - 1 a_(2) = 16 - 1 a_(2) = 15Calculate a_(3): Now that we have a_(2) = 15, we can find a_(3) using the same recursive formula. Calculate a_(3) using a_(2): a_(3) = (a_(2))^2 - 1 a_(3) = (15)^2 - 1 a_(3) = 225 - 1 a_(3) = 224

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

If $a_{1}=4$ and $a_{n}=\left(a_{n-1}\right)^{2}-1$ then find the value of $a_{3}$ . $\newline$ Answer:

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Math Problems

Algebra 2

Evaluate rational expressions II

Full solution

Q. If

a_{1}=4

and

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

then find the value of

a_{3}

\newline

Answer:

Calculate $a_{2}$ : We are given that $a_{1} = 4$ . To find $a_{3}$ , we first need to find $a_{2}$ using the recursive formula $a_{n} = (a_{n-1})^2 - 1$ . $\newline$ Calculate $a_{2}$ using $a_{1}$ : $\newline$ $a_{2} = (a_{1})^2 - 1$ $\newline$ $a_{2} = (4)^2 - 1$ $\newline$ $a_{2} = 16 - 1$ $\newline$ $a_{1} = 4$ $0$
Calculate $a_{3}$ : Now that we have $a_{2} = 15$ , we can find $a_{3}$ using the same recursive formula. $\newline$ Calculate $a_{3}$ using $a_{2}$ : $\newline$ $a_{3} = (a_{2})^2 - 1$ $\newline$ $a_{3} = (15)^2 - 1$ $\newline$ $a_{3} = 225 - 1$ $\newline$ $a_{3} = 224$