Question

Which of these positive integers are terms of the fibonacci sequence, defined recursively by f(0) = 0 f(1) = 1 f(n) = f(n – 1) + f(n – 2), for n > 1?

1) 6
2) 3
3) 4
4) 8
5) 5
6) 7

Answer 1

From the given list of positive integers, the numbers 3, 5, and 8 are terms of the Fibonacci sequence, which is defined by the recurrence relation f(n) = f(n − 1) + f(n − 2) for n > 1.

Step-by-step explanation:

To determine which of the given positive integers are terms of the Fibonacci sequence, defined recursively by f(0) = 0, f(1) = 1 and f(n) = f(n − 1) + f(n − 2) for n > 1, we should list the first few terms of the sequence:

• 0 (f(0))
• 1 (f(1))
• 1 (f(2))
• 2 (f(3))
• 3 (f(4))
• 5 (f(5))
• 8 (f(6))
• 13 (f(7))

Comparing the given numbers with the terms of the Fibonacci sequence, we find that:

• 1) 6 is not a term.
• 2) 3 is a term (f(4)).
• 3) 4 is not a term.
• 4) 8 is a term (f(6)).
• 5) 5 is a term (f(5)).
• 6) 7 is not a term.

Therefore, the positive integers from the given list that are in the Fibonacci sequence are 3, 5, and 8.