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.

Video Examples:Introduction to the Fibonacci sequence
 

Solved Example on Fibonacci Sequence

Ques: 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: ⇒ 79 = A + B --------------- (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: ⇒ 5A + 8B = 542 ------------(2)
Step 11: Solving equations (1) and (2)
5A + 8B = 542
5A + 5B = 395
____________ 
3B = 147
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.