If a_(1)=3 and a_(n)=(a_(n-1))^(2)-5 then find the value of a_(4). Answer:

Given Value: We are given that a_(1) = 3. To find a_(4), we need to find a_(2), a_(3), and then a_(4) using the recursive formula a_(n) = (a_(n-1))^2 - 5.Find a_(2): First, let's find a_(2) using the formula with n=2. a_(2) = (a_(1))^2 - 5 Substitute a_(1) = 3 into the formula. a_(2) = (3)^2 - 5 a_(2) = 9 - 5 a_(2) = 4Find a_(3): Next, we find a_(3) using the formula with n=3. a_(3) = (a_(2))^2 - 5 Substitute a_(2) = 4 into the formula. a_(3) = (4)^2 - 5 a_(3) = 16 - 5 a_(3) = 11Find a_(4): Finally, we find a_(4) using the formula with n=4. a_(4) = (a_(3))^2 - 5 Substitute a_(3) = 11 into the formula. a_(4) = (11)^2 - 5 a_(4) = 121 - 5 a_(4) = 116

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If
a_(1)=3 and
a_(n)=(a_(n-1))^(2)-5 then find the value of
a_(4).
Answer:

If $a_{1}=3$ and $a_{n}=\left(a_{n-1}\right)^{2}-5$ 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}=3

and

a_{n}=\left(a_{n-1}\right)^{2}-5

then find the value of

a_{4}

\newline

Answer:

Given Value: We are given that $a_{1} = 3$ . To find $a_{4}$ , we need to find $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula $a_{n} = (a_{n-1})^2 - 5$ .
Find $a_{2}$ : First, let's find $a_{2}$ using the formula with $n=2$ .
$a_{2} = (a_{1})^2 - 5$
Substitute $a_{1} = 3$ into the formula.
$a_{2} = (3)^2 - 5$
$a_{2} = 9 - 5$
$a_{2} = 4$
Find $a_{3}$ : Next, we find $a_{3}$ using the formula with $n=3$ . $\newline$ $a_{3} = (a_{2})^2 - 5$ $\newline$ Substitute $a_{2} = 4$ into the formula. $\newline$ $a_{3} = (4)^2 - 5$ $\newline$ $a_{3} = 16 - 5$ $\newline$ $a_{3} = 11$
Find $a_{4}$ : Finally, we find $a_{4}$ using the formula with $n=4$ . $\newline$ $a_{4} = (a_{3})^2 - 5$ $\newline$ Substitute $a_{3} = 11$ into the formula. $\newline$ $a_{4} = (11)^2 - 5$ $\newline$ $a_{4} = 121 - 5$ $\newline$ $a_{4} = 116$