Fibonacci Sequence...Part I

It was first observed by the Italian mathematician Leonardo Fibonacci in 1202. He was investigating how fast rabbits could breed under ideal circumstances. He made the following assumptions:
Begin with one male and one female rabbit. Rabbits can mate at the age of one month, so by the end of the second month, each female can produce another pair of rabbits.
The rabbits never die.
The female produces one male and one female every month.
He calculated how many pairs of rabbits would be produced in one year.

Motivate the students to develop the sequence themselves. Remind them that they have to count only the pairs of rabbits and not individual rabbits.

Give them some hint

You begin with one pair of rabbits ,write 1.
At the end of the first month, there is still only one pair ,again write 1.
At the end of the second month, the female has produced a second pair, so there are 2 pairs, write 2.
At the end of the third month, the original female has produced another pair, so now there are 3 pairs.so write 3.
At the end of the fourth month, the original female has produced yet another pair, and the female born two months earlier has produced her first pair, making a total of 5 pairs ,write 5.

Write the pattern that has emerged : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and 233...

Observe what rule is being followed to get from one number to the next.

Understand that to get the next number in the sequence, you have to add the previous two numbers.