Interestingly enough, the Fibonacci numbers appear in quite unexpected places. They occur in nature, music, geography, and geometry. They can be found in the spiral arrangements of seeds in sunflowers, the scale patterns of pine cones, the number of petals in flowers, and the arrangement of leaves on trees. Find the first 25 Fibonacci numbers. The Fibonacci sequence appears in the family tree of a male bee. Male bees hatch from eggs which have not been fertilized, while female bees hatch from fertilized eggs. Because of this, a male bee has only one parent, his mother. On the other hand, female bees have both mothers and fathers. Using for female bees and for male bees, continue the family tree started below back 5 generations. Thus, a male bee has 1 parent, 2 grandparents, 3 great-grandparents, and so on. Solution Fibonacci series: F(n)=F(n-1)+F(n-2) we know that F(0)=F(1)=1 F(2)=F(1)+F(0)=1+1=2 F(3)=F(2)+F(1)=2+1=3 F(4)=F(3)+F(2)=3+2=5 F(5)=F(4)+F(3)=5+3=8 F(6)=F(5)+F(4)=8+5=13 F(7)=F(6)+F(5)=13+8=21 F(8)=F(7)+F(6)=21+13=34 F(9)=F(8)+F(7)=34+21=55 F(10)=F(9)+F(8)=55+34=89 F(11)=F(10)+F(9)=89+55=144 F(12)=F(11)+F(10)=144+89=233 F(13)=F(12)+F(11)=233+144=377 F(14)=F(13)+F(12)=377+233=610 F(15)=F(14)+F(13)=610+377=987 F(16)=F(15)+F(14)=987+610=1597 F(17)=F(16)+F(15)=1597+987=2584 F(18)=F(17)+F(16)=2584+1597=4181 F(19)=F(18)+F(17)=4181+2584=6765 F(20)=F(19)+F(18)=6765+4181=10946 F(21)=F(20)+F(19)=10946+6765=17711 F(22)=F(21)+F(20)=17711+10946=28657 F(23)=F(22)+F(21)=28657+17711=46368 F(24)=F(23)+F(22)=46368+28657=75025 F(25)=F(24)+F(23)+75025+46368=121393.

1. Interestingly enough, the Fibonacci numbers appear in quite unexpected places. They occur in
nature, music, geography, and geometry. They can be found in the spiral arrangements of seeds
in sunflowers, the scale patterns of pine cones, the number of petals in flowers, and the
arrangement of leaves on trees. Find the first 25 Fibonacci numbers. The Fibonacci sequence
appears in the family tree of a male bee. Male bees hatch from eggs which have not been
fertilized, while female bees hatch from fertilized eggs. Because of this, a male bee has only one
parent, his mother. On the other hand, female bees have both mothers and fathers. Using for
female bees and for male bees, continue the family tree started below back 5 generations. Thus,
a male bee has 1 parent, 2 grandparents, 3 great-grandparents, and so on.
Solution
Fibonacci series:
F(n)=F(n-1)+F(n-2)
we know that F(0)=F(1)=1
F(2)=F(1)+F(0)=1+1=2
F(3)=F(2)+F(1)=2+1=3
F(4)=F(3)+F(2)=3+2=5
F(5)=F(4)+F(3)=5+3=8
F(6)=F(5)+F(4)=8+5=13
F(7)=F(6)+F(5)=13+8=21
F(8)=F(7)+F(6)=21+13=34
F(9)=F(8)+F(7)=34+21=55
F(10)=F(9)+F(8)=55+34=89
F(11)=F(10)+F(9)=89+55=144
F(12)=F(11)+F(10)=144+89=233
F(13)=F(12)+F(11)=233+144=377
F(14)=F(13)+F(12)=377+233=610
F(15)=F(14)+F(13)=610+377=987
F(16)=F(15)+F(14)=987+610=1597
F(17)=F(16)+F(15)=1597+987=2584
F(18)=F(17)+F(16)=2584+1597=4181
F(19)=F(18)+F(17)=4181+2584=6765
F(20)=F(19)+F(18)=6765+4181=10946
F(21)=F(20)+F(19)=10946+6765=17711
F(22)=F(21)+F(20)=17711+10946=28657

2. F(23)=F(22)+F(21)=28657+17711=46368
F(24)=F(23)+F(22)=46368+28657=75025
F(25)=F(24)+F(23)+75025+46368=121393