Answer: Choice A
f(1) = 2
f(n) = 2*f(n-1) for n ≥ 2
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Explanation:
n = term number
So for instance, n = 3 represents the index for the 3rd term
We see that when n = 1, f(n) = 2 as shown by the left-most red point.
This means that f(1) = 2 which is a short way of saying "the first term is 2".
So the answer is between A and C.
Let's randomly guess that it might be choice C. We'll use the recursive rule given to generate the next term
f(n) = 4*f(n-1)
f(2) = 4*f(2-1) .... replace every n with 2
f(2) = 4*f(1)
f(2) = 4*2 ..... replace f(1) with 2, since f(1) = 2
f(2) = 8
This tells us that the 2nd term is 8, but the graph says it should be 4. Note the red point at (2,4)
Ultimately this all means that we can eliminate choice C and go with choice A as the final answer.
As a check, let's plug n = 2 into the recursive rule for choice A
f(n) = 2*f(n-1)
f(2) = 2*f(2-1)
f(2) = 2*f(1)
f(2) = 2*2
f(2) = 4
We get the proper second term. I'll let you check the other remaining terms. The notation 2*f(n-1) means "multiply 2 by the previous (n-1) term". In other words, the term values are doubling {2,4,8,16,...}