Honeybee reproduction is an interesting phenomenon. When a queen bee lays an egg, the egg does not need to be fertilized by a male honeybee to hatch. The egg will develop into a male or a female honeybee depending on whether the egg is fertilized by a male honeybee. The outcome is determined by the following rules:
· If an egg is not fertilized, it hatches a drone, or male, honeybee.
· If an egg is fertilized, it hatches a worker, or female, honeybee.

a. Based on this information, how many parents will a drone have?
b. How many grandparents will a drone have?
c. How many great-grandparents, great-great-grandparents, and great-great-great-grandparents will a drone have?
d. Write the numbers together, and determine what type of sequence they form.
e. Write the sequence using a recursive function
f. Use the Internet to research and list at least three other real-world situations that you can model with the Fibonacci sequence.
g. In your research, what famous number or ratio related to the Fibonacci sequence did you come across?

According to the problem, Drones have just mother & no fathers.
Having said that it become easy to solve the problem:

a. Based on this information, how many parents will a drone have? 1

b. How many grandparents will a drone have? 2

c. 1)How many great-grandparents, 3
    2)great-great-grandparents, 5
    3)great-great-great-grandparents will a drone have, 8

d. Write the numbers together, and determine what type of sequence they form:
1,2, 3, 5, 8 (notice that the 3rd term = the sum of the preceding numbers 3=1+2, 5=3+2, 8= 5+3) So it's a Fibonacci sequence

e. Write the sequence using a recursive function: a(n) = a(n-2)+a(n-1)

f. Use the Internet to research: Do it & you will find several related facts

g. In your research, what famous number ...
    Let's take again the Fibonacci sequence:
     1, 2, 3, 5, 8, 13, 21, 34, ...
     Now let's evaluate the ratio between 2 consecutive number:
      3/2 =1.5
      5/3= 1.666
      8/5 = 1.6
      13/8 = 1.625
      21/13 =1.615
      34/21 = 1.619
This ratio tends to be 1.618 which is calle the Golden Ratio