Question

The Fibonacci sequence is F(n) = F(n – 1) + F(n – 2). If F(7) = 13 and F(8) = 21, which of the following is true?\


A. F(6) = 13
B. F(9) = 32
C. F(15) = 34
D. F(9) = 34

Answer 1

Answer:

D. F(9) = 34

Step-by-step explanation:

Given,

F(n) =  F(n – 1) + F(n – 2)

For n = 8,

F(8) = F(8-1) + F(8-2) = F(7) + F(6)

⇒ 13 +  F(6)  = 21 ⇒ F(6) = 5

⇒ Option A is incorrect.

Now, for n = 9,

F(9) =  F(9 – 1) + F(9 – 2)= F(8) + F(7) = 21 + 13 = 34

⇒ Option B is incorrect.

F(15) ≠ F(9)

⇒ F(15) ≠ 34

⇒ Option C is incorrect.

Hence, only option D is correct.