IntroductionWe often come across numbers that follow a particular pattern which enables us to find the next term. One such interesting concept invented by Leonardo Pisa, later known as Fibonacci (Fibonacci Series) helps us in the study of natural happenings like branching of plants, leaves and petal arrangement, reproduction rates of rabbits etc.
Fibonacci sequence is 1, 1, 2, 3, 5, 8....... Can you guess what the next number is? (The next number will be 8 + 5 = 13)
Let us consider some simple examples:
- The Fibonacci sequence is seen in the reproductive pattern of honey bee.
- As we walk up or down stairs, sometimes we unconsciously count the steps. If each step rises by 16cm and we climb 10 steps of a stair-way up, we would have gone up by 160 cm totally. One step takes us 16cm up, 2 steps 32 cm and so on. This forms a pattern: 16, 32, 48,...., 160. You might recollect that this is an arithmetic progression (already done in earlier class) with a common difference of 16.
- A ball is dropped from a height of 6 metres, and on each bounce, it rises of the previous height.
This follow the pattern: 6, 4, 4, After a long time, the ball comes to rest and we can use a mathematical formula to determine the total distance covered by the ball. (We shall see this later in this Chapter)
Some more examples of patterns of numbers
- 6, 16, 26, 36...
- 1, 3, 9, 27...
- 1, 6, 16, 36, 76... (Multiply by 2 and add 4 to it to get the next number)
- 10, 8, 6, 4...
- 0.4, 0.44, 0.444.... (dots are decimals)
- (dots stand for multiplication)