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

Given value and formula: We are given that a_(1) = 1. To find a_(4), we need to find the values of a_(2), a_(3), and then a_(4) using the recursive formula a_(n) = (a_(n-1))^2 - n.Find a_(2): First, let's find a_(2) using the formula with n = 2. a_(2) = (a_(1))^2 - 2 a_(2) = (1)^2 - 2 a_(2) = 1 - 2 a_(2) = -1Find a_(3): Next, we find a_(3) using the formula with n = 3 and the previously found value of a_(2). a_(3) = (a_(2))^2 - 3 a_(3) = (-1)^2 - 3 a_(3) = 1 - 3 a_(3) = -2Find a_(4): Finally, we find a_(4) using the formula with n = 4 and the previously found value of a_(3). a_(4) = (a_(3))^2 - 4 a_(4) = (-2)^2 - 4 a_(4) = 4 - 4 a_(4) = 0

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

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

then find the value of

a_{4}

\newline

Answer:

Given value and formula: We are given that $a_{1} = 1$ . To find $a_{4}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula $a_{n} = (a_{n-1})^2 - n$ .
Find $a_{2}$ : First, let's find $a_{2}$ using the formula with $n = 2$ .
$a_{2} = (a_{1})^2 - 2$
$a_{2} = (1)^2 - 2$
$a_{2} = 1 - 2$
$a_{2} = -1$
Find $a_{3}$ : Next, we find $a_{3}$ using the formula with $n = 3$ and the previously found value of $a_{2}$ .
$a_{3} = (a_{2})^2 - 3$
$a_{3} = (-1)^2 - 3$
$a_{3} = 1 - 3$
$a_{3} = -2$
Find $a_{4}$ : Finally, we find $a_{4}$ using the formula with $n = 4$ and the previously found value of $a_{3}$ .
$a_{4} = (a_{3})^2 - 4$
$a_{4} = (-2)^2 - 4$
$a_{4} = 4 - 4$
$a_{4} = 0$