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

Given Initial Condition: We are given the initial condition f(1) = 4 and the recursive formula f(n) = f(n-1)^(2) - 5. To find f(3), we first need to find f(2).Find f(2): Using the recursive formula, we substitute n = 2 to find f(2): f(2) = f(2-1)^(2) - 5 f(2) = f(1)^(2) - 5 f(2) = 4^(2) - 5 f(2) = 16 - 5 f(2) = 11Find f(3): Now that we have f(2), we can use it to find f(3) using the same recursive formula: f(3) = f(3-1)^(2) - 5 f(3) = f(2)^(2) - 5 f(3) = 11^(2) - 5 f(3) = 121 - 5 f(3) = 116

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

If $f(1)=4$ and $f(n)=f(n-1)^{2}-5$ then find the value of $f(3)$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=4

and

f(n)=f(n-1)^{2}-5

then find the value of

f(3)

\newline

Answer:

Given Initial Condition: We are given the initial condition $f(1) = 4$ and the recursive formula $f(n) = f(n-1)^{2} - 5$ . To find $f(3)$ , we first need to find $f(2)$ .
Find $f(2)$ : Using the recursive formula, we substitute $n = 2$ to find $f(2)$ :
$f(2) = f(2-1)^{2} - 5$
$f(2) = f(1)^{2} - 5$
$f(2) = 4^{2} - 5$
$f(2) = 16 - 5$
$f(2) = 11$
Find $f(3)$ : Now that we have $f(2)$ , we can use it to find $f(3)$ using the same recursive formula: $\newline$ $f(3) = f(3-1)^{2} - 5$ $\newline$ $f(3) = f(2)^{2} - 5$ $\newline$ $f(3) = 11^{2} - 5$ $\newline$ $f(3) = 121 - 5$ $\newline$ $f(3) = 116$