Question

A fibonacci series is:
A. series of numbers in which each number (fibonacci number) is the sum of the two preceding numbers
B. The simplest is the series 1, 1, 2, 3, 5, 8, etc.
C. Both are correct
D. None is correct.

Answer 1

Hint: In a fibonacci series, the first and second terms must be given manually and starting from the third term the rest of the terms of the series can be obtained automatically. The terms starting from the third term are obtained by adding the two preceding consecutive terms in a fibonacci series.

Complete step-by-step answer:
We are given to find the definition of a fibonacci series.
Fibonacci series is a series of numbers formed by adding the preceding two numbers of the same series.
The original Fibonacci series starts with 0 as the first term and 1 as the second term. Then the third term is obtained by adding 1st and 2nd terms which is 0+1=1, 3rd term is 1.
4th term is obtained by adding 2nd and 3rd terms which is 1+1=2, 4th term is 2.
The 5th term is obtained by adding 3rd and 4th terms which is 1+2=3, 5th term is 3.
The resulting fibonacci series will be 0, 1, 1, 2, 3, 5, 8 ……
The series 1, 1, 2, 3, 5, 8, etc is also a fibonacci series and it is the subset of the original fibonacci series because it did not start with 0.
Therefore, a series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers is a fibonacci series and the simplest is the series 1, 1, 2, 3, 5, 8, etc.

So, the correct answer is “Option C”.

Note: A fibonacci series is not the same as an arithmetic series, because the difference between two consecutive terms in an arithmetic series is always constant (common difference) whereas it varies constantly in a fibonacci series.