anonymous
  • anonymous
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) = ______
Mathematics
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anonymous
  • anonymous
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) = ______
Mathematics
chestercat
  • chestercat
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Vocaloid
  • Vocaloid
do you understand what f(n) = f(1) + f(2) + f(n - 1) means?
anonymous
  • anonymous
nope
Vocaloid
  • Vocaloid
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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anonymous
  • anonymous
somewhat
Astrophysics
  • Astrophysics
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.
Astrophysics
  • Astrophysics
So what is f(4)?
anonymous
  • anonymous
5-1?
Astrophysics
  • Astrophysics
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)...
Astrophysics
  • Astrophysics
\[f(5) = f(1)+f(2)+f(1)+f(2)+f(3)\] so this is what we have so far, we need to find f(3), I think you should be able to do the rest.
Empty
  • Empty
It's probably best to just plug in f(1) and f(2) from the very start to get the new recurrence relation: f(n+1)=f(n)+7

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