Find f(5) for this sequence
f(1) = 2 and f(2) = 5, f(n) = f(1) + f(2) + f(n - 1), for n > 2.
f(5) = ______
Stacey Warren - Expert brainly.com
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do you understand what
f(n) = f(1) + f(2) + f(n - 1)
f(n) = f(1) + f(2) + f(n - 1) is a rule we can use to find the value of the function for a certain n value
so, let's just say we want to find f(3), where n = 3
we can use the formula
f(n) = f(1) + f(2) + f(n-1), giving us
f(3) = f(1) + f(2) + f(3-1), does that make sense so far?
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Ok so I think you're still kind of confused on what to do after you plug in n = 5, so we have \[f(5) = f(1)+f(2)+f(5-1) \implies f(5)=f(1)+f(2)+f(4)\] but notice we don't have f(4) given right? We have to figure that out using the same formula.
So what is f(4)?
I mean you have to use the same formula \[f(4) = f(1)+f(2)+f(4-1) \implies f(1)+f(2)+f(3)\] so now we need to find f(3)...
\[f(5) = f(1)+f(2)+f(1)+f(2)+f(3)\] so this is what we have so far, we need to find f(3), I think you should be able to do the rest.
It's probably best to just plug in f(1) and f(2) from the very start to get the new recurrence relation: