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

Given sequence: Given the recursive sequence: a_(1) = 3 a_(n+1) = (a_(n))^2 + 2 We need to find the value of a_(4). First, let's find a_(2) using the given formula. a_(2) = (a_(1))^2 + 2Calculate a_(2): Now we calculate a_(2) using the value of a_(1) which is 3. a_(2) = (3)^2 + 2 a_(2) = 9 + 2 a_(2) = 11Find a_(3): Next, we find a_(3) using the value of a_(2). a_(3) = (a_(2))^2 + 2 a_(3) = (11)^2 + 2Calculate a_(3): We calculate a_(3) using the value of a_(2) which is 11. a_(3) = 121 + 2 a_(3) = 123Find a_(4): Finally, we find a_(4) using the value of a_(3). a_(4) = (a_(3))^2 + 2 a_(4) = (123)^2 + 2Calculate a_(4): We calculate a_(4) using the value of a_(3) which is 123. a_(4) = 15129 + 2 a_(4) = 15131

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Math Problems

Algebra 2

Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. If

a_{1}=3

and

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

then find the value of

a_{4}

\newline

Answer:

Given sequence: Given the recursive sequence: $\newline$ $a_1 = 3$ $\newline$ $a_{n+1} = a_n^2 + 2$ $\newline$ We need to find the value of $a_4$ . $\newline$ First, let's find $a_2$ using the given formula. $\newline$ $a_2 = a_1^2 + 2$
Calculate $a_{2}$ : Now we calculate $a_{2}$ using the value of $a_{1}$ which is $3$ . $\newline$ $a_{2} = (3)^2 + 2$ $\newline$ $a_{2} = 9 + 2$ $\newline$ $a_{2} = 11$
Find $a_{3}$ : Next, we find $a_{3}$ using the value of $a_{2}$ .
$a_{3} = (a_{2})^2 + 2$
$a_{3} = (11)^2 + 2$
Calculate $a_{3}$ : We calculate $a_{3}$ using the value of $a_{2}$ which is $11$ . $\newline$ $a_{3} = 121 + 2$ $\newline$ $a_{3} = 123$
Find $a_{4}$ : Finally, we find $a_{4}$ using the value of $a_{3}$ .
$a_{4} = (a_{3})^2 + 2$
$a_{4} = (123)^2 + 2$
Calculate $a_{4}$ : We calculate $a_{4}$ using the value of $a_{3}$ which is $123$ . $\newline$ $a_{4} = 15129 + 2$ $\newline$ $a_{4} = 15131$