Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Numerical Answers Expected!

Answer 1

@satellite73

Answer 2

@zepdrix

Answer 3

@Opcode

Answer 4

\[\Large\rm f(1)=2\]\[\Large\rm f(2)=3\]\[\Large\rm f(\color{orangered}{n})=f(1)+f(2)+f(\color{orangered}{n}-1)\]Let's start by finding f(3), using this recursive formula.

Answer 5

\[\Large\rm f(\color{orangered}{3})=f(1)+f(2)+f(\color{orangered}{3}-1)\]

Answer 6

After simplifying, we see that our third term is given by this:
\[\Large\rm f(3)=f(1)+f(2)+f(2)\]

Answer 7

actually im kinda llost

Answer 8

Notice that for this relationship,\[\Large\rm f(\color{orangered}{n})=f(1)+f(2)+f(\color{orangered}{n}-1)\]Our Nth term is recursively related to the (N-1)th term, the term previous to N.
But the f(1) and f(2) are the first two terms, those are given to us.
Maybe we should plug them in to simplify the formula a little bit.

Answer 9

\[\Large\rm f(\color{orangered}{n})=2+3+f(\color{orangered}{n}-1)\]\[\Large\rm f(\color{orangered}{n})=5+f(\color{orangered}{n}-1)\]

Answer 10

So our relationship is showing us that the next term in the sequence will always be `5 more than the previous term`.

Answer 11

oh made it easier ;)

Answer 12

\[\Large\rm f(\color{orangered}{n})=5+f(\color{orangered}{n}-1)\]We're plugging in 3 for our n.
That's what will give us f(3), our third term.

Answer 13

\[\Large\rm f(\color{orangered}{3})=5+f(\color{orangered}{3}-1)\]The 3-1 simplifies to 2.

Answer 14

\[\Large\rm f(3)=5+f(2)\]This is telling us that the third term is 5 more than the second term.

Answer 15

So what do we get for the third term?
Do you remember what the second term was? We just need to add 5 to that.