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

Given Sequence and Formula: We are given the first term of the sequence, a_(1) = 1, and the recursive formula a_(n+1) = (a_(n))^2 - 3. We need to find the value of a_(4).Find a_(2): First, let's find a_(2) using the recursive formula with n = 1. a_(2) = (a_(1))^2 - 3 = (1)^2 - 3 = 1 - 3 = -2.Find a_(3): Next, we find a_(3) using the recursive formula with n = 2. a_(3) = (a_(2))^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1.Find a_(4): Finally, we find a_(4) using the recursive formula with n = 3. a_(4) = (a_(3))^2 - 3 = (1)^2 - 3 = 1 - 3 = -2.

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

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

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Math Problems

Algebra 2

Evaluate rational expressions II

Full solution

Q. If

a_{1}=1

and

a_{n+1}=\left(a_{n}\right)^{2}-3

then find the value of

a_{4}

\newline

Answer:

Given Sequence and Formula: We are given the first term of the sequence, $a_{1} = 1$ , and the recursive formula $a_{n+1} = (a_{n})^2 - 3$ . We need to find the value of $a_{4}$ .
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula with $n = 1$ . $\newline$ $a_{2} = (a_{1})^2 - 3 = (1)^2 - 3 = 1 - 3 = -2$ .
Find $a_{3}$ : Next, we find $a_{3}$ using the recursive formula with $n = 2$ . $\newline$ $a_{3} = (a_{2})^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1$ .
Find $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula with $n = 3$ . $\newline$ $a_{4} = (a_{3})^2 - 3 = (1)^2 - 3 = 1 - 3 = -2$ .