Suk-Sci said:T.P.T : a2n=an*bn
The Fibonacci Series is a sequence of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. The series goes like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... and so on.
The Lucas Series is a similar sequence of numbers, but it starts with 2 and 1 instead of 0 and 1. So the series goes like this: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... and so on.
The Lucas Series is a generalization of the Fibonacci Series, meaning that it follows the same pattern but with different starting numbers. Both series also share a mathematical formula for calculating any number in the sequence.
Fibonacci and Lucas Series can be observed in many natural phenomena, such as the branching of trees, the arrangement of leaves on a stem, and the spiral patterns of shells and flowers. This is because these series represent efficient growth patterns and can be found in many living organisms.
Fibonacci and Lucas Series have numerous applications in mathematics, including number theory, geometry, and algebra. They also have practical uses in fields such as computer science, finance, and biology. For example, the Fibonacci sequence is often used in coding and data compression, while the Lucas sequence is used in cryptography and prime number generation.