Understanding the Recursive Nature of the Fibonacci Sequence

The video tutorial explains the Fibonacci sequence as a recursive sequence, where each term is the sum of the two preceding ones. It contrasts this with a general recursive sequence, which adds a constant difference to each term. The video clarifies common misconceptions about the Fibonacci sequence and demonstrates how to calculate specific terms using its unique recursive rule. The tutorial concludes by calculating the 9th and 10th terms of the Fibonacci sequence.

What is a key characteristic of a recursive sequence?

• The sequence has a fixed number of terms.

• Each term is used to find the next term.

• Each term is independent of the others.

• The sequence is always increasing.

In the example of a simple recursive sequence, what is added to each term to find the next?

• 3

• 4

• 5

• 2

What is the recursive rule for the Fibonacci sequence?

• a_n = a_(n-2) + 2

• a_n = a_(n-1) + 4

• a_n = a_(n-1) + 1

• a_n = a_(n-1) + a_(n-2)

Why does the Fibonacci sequence not follow the general recursive rule?

• It has a common difference of 1.

• It adds the previous two terms to find the next term.

• It has a fixed number of terms.

• It is not a sequence.

What is the 9th term of the Fibonacci sequence?

• 34

• 21

• 13

• 8

How is the 10th term of the Fibonacci sequence calculated?

• By adding the 6th and 7th terms.

• By adding the 9th and 10th terms.

• By adding the 8th and 9th terms.

• By adding the 7th and 8th terms.

What is the 10th term of the Fibonacci sequence?

• 13

• 55

• 34

• 21