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

Calculate a_(2): Given the recursive formula a_(n)=(a_(n-1))^(2)+n and the initial condition a_(1)=2, we need to find the value of a_(4). We will start by finding a_(2) using the given formula. a_(2) = (a_(1))^2 + 2 = (2)^2 + 2 = 4 + 2 = 6Calculate a_(3): Next, we will find a_(3) using the value of a_(2) we just calculated. a_(3) = (a_(2))^2 + 3 = (6)^2 + 3 = 36 + 3 = 39Calculate a_(4): Finally, we will find a_(4) using the value of a_(3). a_(4) = (a_(3))^2 + 4 = (39)^2 + 4 = 1521 + 4 = 1525

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

If $a_{1}=2$ 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 expression when a complex numbers and a variable term is given

Full solution

Q. If

a_{1}=2

and

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

then find the value of

a_{4}

\newline

Answer:

Calculate $a_{2}$ : Given the recursive formula $a_{n}=(a_{n-1})^{2}+n$ and the initial condition $a_{1}=2$ , we need to find the value of $a_{4}$ . We will start by finding $a_{2}$ using the given formula. $\newline$ $a_{2} = (a_{1})^2 + 2$ $\newline$ $= (2)^2 + 2$ $\newline$ $= 4 + 2$ $\newline$ $= 6$
Calculate $a_{3}$ : Next, we will find $a_{3}$ using the value of $a_{2}$ we just calculated. $\newline$ a_{3} = (a_{2})^2 + 3$\newline = (6)^2 + 3 $\newline$ = 36 + 3 $\newline$ = 39$
Calculate $a_{4}$ : Finally, we will find $a_{4}$ using the value of $a_{3}$ . $a_{4} = (a_{3})^2 + 4 = (39)^2 + 4 = 1521 + 4 = 1525$