Answer: 52
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Step-by-step 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.
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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.