Calculating the Fibonacci sequence
Any Fibonacci number can be calculated by using this formula,
xn = (φn − (1−φ)n)/√5
- xn denotes Fibonacci number to be calculated
- φ is Golden ratio that is 1.618034
For example: If you want to calculate the 7th term:
x7 = ((1.618034)7-(1-1.618034)7)/√5
x7 = 13.0000007
x7 = 13(rounded off)
Next Fibonacci number can also be calculated using Golden Ratio. Multiplying a Fibonacci number with a golden ratio will give the next Fibonacci number of the sequence. But that only works for numbers greater than 1.
Example: 13 × 1.618034 = 21.034442 = 21(rounded off)
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Fibonacci Sequence Formula
Fibonacci Sequence Formula: Fibonacci sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, …, each of which, after the second, is the sum of the two previous numbers; that is, the nth Fibonacci number Fn = Fn − 1 + Fn − 2.
In the Fibonacci sequence, each number in the series is calculated by adding the two numbers before it. Generally, the first two terms of the Fibonacci series are 0 and 1. The Fibonacci sequence was known in India hundreds of years before Leonardo Pisano Bigollo knew about it. November 23rd is celebrated as Fibonacci Day, as it has the digits “1, 1, 2, 3” which is part of the sequence
In this article, we will learn about the Fibonacci Sequence, along with its formula, examples, golden ratio, etc.
Fibonacci Sequence Formula
Table of Content
- What is the Fibonacci Sequence?
- Fibonacci Sequence Formula
- Golden Ratio
- Calculating the Fibonacci sequence
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence Formula
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