If a_(1)=4 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) = 4. We need to find 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. a_(2) = (a_(1))^2 - 2 Substitute a_(1) = 4 into the formula. a_(2) = (4)^2 - 2 a_(2) = 16 - 2 a_(2) = 14Find a_(3): Next, we find a_(3) using the formula and the value of a_(2). a_(3) = (a_(2))^2 - 3 Substitute a_(2) = 14 into the formula. a_(3) = (14)^2 - 3 a_(3) = 196 - 3 a_(3) = 193Find a_(4): Finally, we find a_(4) using the formula and the value of a_(3). a_(4) = (a_(3))^2 - 4 Substitute a_(3) = 193 into the formula. a_(4) = (193)^2 - 4 a_(4) = 37249 - 4 a_(4) = 37245

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

If $a_{1}=4$ 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}=4

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 $a_{1} = 4$ . We need to find $a_{4}$ using the recursive formula $a_{n} = (a_{n-1})^2 - n$ .
Find $a_{2}$ : First, let's find $a_{2}$ using the formula. $\newline$ $a_{2} = (a_{1})^2 - 2$ $\newline$ Substitute $a_{1} = 4$ into the formula. $\newline$ $a_{2} = (4)^2 - 2$ $\newline$ $a_{2} = 16 - 2$ $\newline$ $a_{2} = 14$
Find $a_{3}$ : Next, we find $a_{3}$ using the formula and the value of $a_{2}$ .
$a_{3} = (a_{2})^2 - 3$
Substitute $a_{2} = 14$ into the formula.
$a_{3} = (14)^2 - 3$
$a_{3} = 196 - 3$
$a_{3} = 193$
Find $a_{4}$ : Finally, we find $a_{4}$ using the formula and the value of $a_{3}$ .
$a_{4} = (a_{3})^2 - 4$
Substitute $a_{3} = 193$ into the formula.
$a_{4} = (193)^2 - 4$
$a_{4} = 37249 - 4$
$a_{4} = 37245$