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

Find a_(2): We are given the first term of the sequence, a_(1) = 1. We need to find the value of a_(4). The recursive formula to find the next term is a_(n+1) = (a_(n))^2 - 1. Let's start by finding a_(2).Find a_(3): Using the recursive formula, we calculate a_(2) as follows: a_(2) = (a_(1))^2 - 1 = (1)^2 - 1 = 1 - 1 = 0.Find a_(4): Next, we find a_(3) using the value of a_(2): a_(3) = (a_(2))^2 - 1 = (0)^2 - 1 = 0 - 1 = -1.Finally, we find a_(4) using the value of a_(3): a_(4) = (a_(3))^2 - 1 = (-1)^2 - 1 = 1 - 1 = 0.

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

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

and

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

then find the value of

a_{4}

\newline

Answer:

Find $a_{2}$ : We are given the first term of the sequence, $a_{1} = 1$ . We need to find the value of $a_{4}$ . The recursive formula to find the next term is $a_{n+1} = (a_{n})^2 - 1$ . Let's start by finding $a_{2}$ .
Find $a_{3}$ : Using the recursive formula, we calculate $a_{2}$ as follows: $\newline$ $a_{2} = (a_{1})^2 - 1 = (1)^2 - 1 = 1 - 1 = 0$ .
Find $a_{4}$ : Next, we find $a_{3}$ using the value of $a_{2}$ : $a_{3} = (a_{2})^2 - 1 = (0)^2 - 1 = 0 - 1 = -1$ .
Find $a_{4}$ : Next, we find $a_{3}$ using the value of $a_{2}$ : $a_{3} = (a_{2})^2 - 1 = (0)^2 - 1 = 0 - 1 = -1$ .Finally, we find $a_{4}$ using the value of $a_{3}$ : $a_{4} = (a_{3})^2 - 1 = (-1)^2 - 1 = 1 - 1 = 0$ .