OpenStudy (anonymous):

1,3,4,7,11,... what is the next sequence number?

7 years ago

Can you find a relationship between 4 and its previous two numbers? What about 7 and its previous two numbers?

7 years ago
OpenStudy (michael):

is 18

7 years ago
OpenStudy (anonymous):

ok.i get it.but how to make the formula?

7 years ago
OpenStudy (michael):

a_n=a_{n-1}+a_{n-2}

7 years ago
OpenStudy (michael): 7 years ago
OpenStudy (anonymous):

michael are you study computer science?

7 years ago

Note that the relation is the same as that of the Fibonacci numbers, but these are not the fibonacci numbers, because the sequence starts at 1 and 3, not at 0-1-1 (or 1-1).

7 years ago
OpenStudy (anonymous):

so what we call that number?

7 years ago

There's no special name for these numbers, they just happen to be related in that term number $$n$$ of the relation is defined as the sum of the previous two terms.

7 years ago
OpenStudy (anonymous):

sorry,can i ask you about recursive function? i really dont understand.. hope you can help me..

7 years ago

Sure, what do you need?

7 years ago
OpenStudy (anonymous):

what is recursive function? what i know just it will recall itself. is it?

7 years ago

From a computer science perspective, yes, that's correct. A recursive function is a function that calls itself. Generally speaking, recursive functions have a base case' which, when true, makes the function not call itself. That is how they avoid calling themselves infinitely. For example, in the case of the fibonacci numbers, the base case is having 0 and 1 -- the result is then 1, without having to look at anything else.

7 years ago
OpenStudy (anonymous):

example else of 'base case'? the easier one. actaualy i do not understand the base case.

7 years ago

Well, briefly, if we were to write a function for fibonacci (a bad example, honestly, because writing it recursively is a bit slow, bit it will do) that returns the n-th fibonacci number, we would do: function fibonacci(n): if n == 1 or n == 0 then return 1 else return fibonacci(n - 2) + fibonacci(n - 1) We should also technically take care of n being less than zero, in which case we can answer `undefined' or some such, but that's beside the point. The point here is, if I ask for the 1st fibonacci number, I will get 1. If I ask for the second fibonacci number, I will get the 0th fibonacci number + the 1st fibonacci number, both of which are defined as one, so I will get 2. If I ask for the third, I will get the 1st fibonacci number + the 2nd fibonacci number, which we defined above as the 0th fibonacci number + the 1st fibonacci number, so we will get 3 (1 + 2). And so on and so forth.

7 years ago
OpenStudy (anonymous):

oh. i get it. thank you so much. hope it will help me on final.

7 years ago

7 years ago
OpenStudy (anonymous):

but later can i ask you more about something like this? my course related to this topic.

7 years ago