If f(1) = 2 and f(n) = f(n − 1)^2 + 3 then find the value of f(3).

Explanation:

Let's use the recursive rule to find f(2)

We'll plug n = 2 into the second equation to find that...

f(n) = ( f(n-1) )^2 + 3

f(2) = ( f(2-1) )^2 + 3

f(2) = ( f(1) )^2 + 3

f(2) = ( 2 )^2 + 3

f(2) = 4 + 3

f(2) = 7

Notice in the jump from lines 3 to 4, we go from f(1) to 2. So f(2) is dependent on what f(1) is.

In other words, the second term is dependent on the first term.

Likewise, f(3) is dependent on f(2)

Plug n = 3 into the recursive definition to find the following

f(n) = ( f(n-1) )^2 + 3

f(3) = ( f(3-1) )^2 + 3

f(3) = ( f(2) )^2 + 3

f(3) = ( 7 )^2 + 3

f(3) = 49 + 3

f(3) = 52

The third term of this recursive sequence is 52.

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.