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) = ______

Question

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) = ______

vocaloid · Answer

do you understand what 

f(n) = f(1) + f(2) + f(n - 1)

means?

anonymous · Answer

nope

vocaloid · Answer

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?

anonymous · Answer

somewhat

astrophysics · Answer

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 · Answer

So what is f(4)?

anonymous · Answer

5-1?

astrophysics · Answer

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 · Answer

$$f(5) = f(1)+f(2)+f(1)+f(2)+f(3)$$ 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 · Answer

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