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A recursive sequence uses previous numbers to find the next number in a sequence after the base case. The Fibonacci sequence is an example of such a sequence. The base numbers of the Fibonacci sequence are 0 and 1. After that base, you find the next number in the sequence by adding the two previous numbers. So, the Fibonacci sequence looks like so:

0, 1, 1, 2, 3, 5, 8....

So, the third number is found by adding the first and second numbers, 0 and 1. So the third number is 1. The fourth number is found by adding the second and third numbers, 1 and 1. So, the fourth number is 2. You can continue on this way forever.

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Q: What is a recursive sequence and its relationship to a Fibonacci sequence.?
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Related questions

Why is Fibonacci recursive?

Each term, except the first two, in the Fibonacci sequence is defined in terms of terms that went earlier in the sequence. That is the meaning of "recursive". t(1) = 1 t(2) = 1 t(n+2) = t(n) + t(n+1) for n = 1, 2, 3, ...


Do grapes come under Fibonacci sequence?

No. Grapes have nothing to do with a recursive series of numbers following the rule that any number is the sum of the previous two.


When did Fibonacci discover the Fibonacci sequence?

Leonardo Fibonacci discovered the Fibonacci sequence In the 12th century.


What is the recursive formula for 2 1 3 4 7 11?

It look like a Fibonacci sequence seeded by t1 = 2 and t2 = 1. After that the recursive formula is simply tn+1 = tn-1 + tn.


Why is the Fibonacci sequence named after Fibonacci?

Leonardo Fibonacci discovered the number sequence which is named after him.


Recursive rule for the Fibonacci sequence?

x1=0 x2=1 for i > 2, xi= xi-1 + xi-2


What are the ninth and tenth numbers in the Fibonacci sequence?

The 9th number in the Fibonacci Sequence is 34, and the 10th number in the Fibonacci sequence is 89.


Who was Leonardo Fibonacci?

Leonardo Fibonacci was the father and creator of the fibonacci sequence a very famous mathematic sequence


How did Fibonacci get his idea for the Fibonacci Sequence?

The Fibonacci Sequence itself was not CREATED by Leonardo of Pisa (more commonly known as Leonardo Fibonacci or simply Fibonacci). He is credited to the introduction of the sequence to the western world, (Hence the name "The Fibonacci Sequence"); however origins of the Fibonacci can be traced back to 200BC. *TJB*


Why did Fibonacci think of the Fibonacci code?

There is the Fibonacci sequence but what is the Fibonacci code?


Why did Fibonacci create the Fibonacci Sequence?

Leonardo Fibonacci did not create the Fibonacci Sequence -- he discovered it during his studies as a mathematician.


What is the 16th number of the Fibonacci sequence?

The 16th number of the Fibonacci sequence is 987.


What is the 20th Fibonacci number in the sequence?

The 20th Fibonacci number in the sequence is 6,765.


How is the value of any term calculated if the position of term is known?

A sequence usually has a position-to-value function. Alternatively, it can be derived from the recursive relationship that defines the sequence.


What name is given to this sequence 11235813?

It is called a Fibonacci number sequence! 1,1,2,3,5,8,13,21...


What is a Fibonacci sequence using 84?

The Fibonacci sequence requires two numbers as "seeds".


What is the Fibonacci sequence used for?

The Fibonacci sequence is used for many calculations in regards to nature. The Fibonacci sequence can help you determine the growth of buds on trees or the growth rate of a starfish.


How would one describe a Fibonacci number?

A Fibonacci number, Fibonacci sequence or Fibonacci series are a mathematical term which follow a integer sequence. The first two numbers in Fibonacci sequence start with a 0 and 1 and each subsequent number is the sum of the previous two.


How do you get the Fibonacci sequence?

Start with 1 and 2. Then each number in the Fibonacci sequence is the sum of the previous two numbers in the sequence.


What is the Fibonacci sequence of twenty-two?

The Fibonacci sequence requires two initial numbers to be specified.


Who pioneered the finonacci sequence?

Not sure about the finonacci sequence but the Fibonacci sequence was discovered and studies by Fibonacci, also known as Leonardo of Pisa.


What is the 24th Fibonacci number?

Assuming the Fibonacci sequence starts with the numbers 0, 1, as per sequence A000045, the 24th Fibonacci number is 28657.


How old was Fibonacci when he discovered the Fibonacci sequence?

42


Is the Fibonacci Sequence named after Leonardo Fibonacci?

Yes.


Is The Fibonacci sequence arithmetic?

No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant