How many terms we need to know to determine a pattern

GRE Quant Problem Solving
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For this question, the answer is the relationship cannot be determined, while I had answered it to be the quantity is equal (i.e., 22) ; according to the explanation we can’t infer a pattern out of only 2 terms f(6) and f(18). But what if I found f(54) by taking 3 times f(18) and the answer is 99? Doesn’t that count as a third term and I can compare all 3 to find a pattern?

f(6) = 11
f(18) = 3 f(6) = 33
f(54) = 3 f(18) = 99
Therefore, every “+6” will cause +11 to be added to the output? Thus f(12) = 11 + 11 = 22?

2

You need to be quite careful here - this is not a sequence problem where it’s easier to assume patterns like the one you did.

A function in its core does only two things: give it an input and it spits out an output. Think about it with that in mind.

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ok, thanks