Fibonacci Sequence

Definition of Fibonacci Sequence

• Fibonacci sequence is an infinite sequence in which the first two terms are 1 and from the third term onwards, each term is formed by adding the previous two terms.

1, 1, 2, 3, 5, 8, 13, . . .  is the Fibonacci sequence.

Solved Example on Fibonacci Sequence

Like the fibonacci sequence 1, 1, 2, 3, 5, 8, . . . . a certain turkey flock has as many turkeys on a given day as the sum of the number of turkeys on the previous 2 days. If there were 79 turkeys on November 7th, and 542 turkeys on November 11th, how many turkeys were there on November 18th?

Choices:

A. 9,726

B. 15,737

C. 5,423

D. 25,463

Correct Answer: B

Solution:

Step 1: Let A be the number of turkeys on November 5th.

Step 2: Let B be the number of turkeys on November 6th.

Step 3: Given that the number of turkeys on a given day is the sum of the number of turkeys on the previous 2 days.

Step 4: Number of turkeys on November 7th = Number of turkeys on November 5th + Number of turkeys on November 6th.

Step 5:  --------------- (1)

Step 6: Similarly the number of turkeys on November 8th = B + A + B = A + 2B

Step 7: Number of turkeys on November 9th = A + B + A + 2B = 2A + 3B

Step 8: Number of turkeys on November 10th = 2A +3B +A +3B = 3A + 5B

Step 9: Number of turkeys on November 11th = 2A + 3B + 3A + 5B = 5A + 8B

Step 10: ------------(2)

Step 11: Solving equations (1) and (2)


____________
 
B = 49 then A = 30

Step 12: We get 30, 49, 79, 128, 207, 335, 542, 877,1419, 2296, 3715, 6011, 9726, 15737, .........

Step 13: Therefore, there are 15737 turkeys on November 18th.

    

Related Terms for Fibonacci Sequence

• Sequence
• Infinite
• Term

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