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

Find a_(2): To find the value of a_(3), we need to first find the value of a_(2) using the given recursive formula a_(n)=(a_(n-1))^2+n. Given a_(1)=3, we substitute n=2 into the formula to find a_(2). a_(2) = (a_(1))^2 + 2 = (3)^2 + 2 = 9 + 2 = 11Calculate a_(3): Now that we have the value of a_(2), we can find a_(3) using the same recursive formula. Substitute n=3 and a_(2)=11 into the formula to find a_(3). a_(3) = (a_(2))^2 + 3 = (11)^2 + 3 = 121 + 3 = 124

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

If $a_{1}=3$ and $a_{n}=\left(a_{n-1}\right)^{2}+n$ then find the value of $a_{3}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=3

and

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

then find the value of

a_{3}

\newline

Answer:

Find $a_{2}$ : To find the value of $a_{3}$ , we need to first find the value of $a_{2}$ using the given recursive formula $a_{n}=(a_{n-1})^2+n$ . $\newline$ Given $a_{1}=3$ , we substitute $n=2$ into the formula to find $a_{2}$ . $\newline$ $a_{2} = (a_{1})^2 + 2$ $\newline$ $= (3)^2 + 2$ $\newline$ $= 9 + 2$ $\newline$ $a_{3}$ $0$
Calculate $a_{3}$ : Now that we have the value of $a_{2}$ , we can find $a_{3}$ using the same recursive formula. $\newline$ Substitute $n=3$ and $a_{2}=11$ into the formula to find $a_{3}$ . $\newline$ $a_{3} = (a_{2})^2 + 3$ $\newline$ $= (11)^2 + 3$ $\newline$ $= 121 + 3$ $\newline$ $= 124$