![]() For larger terms the ratio of two consecutive terms of the Fibonacci Sequence converges to the Golden Ratio, this can be understood by the table added below,.Here the ratio so obtained is called the golden ratio. We can calculate the golden ratio using the above formula, using the Fibonacci sequenceį 11 /F 10 = 89/55 = 1.618 (Golden Ratio) Φ = F n /F n-1 Using The Golden Ratio to Calculate Fibonacci Numbers It is denoted using the Greek symbol “ Φ “. We have observed that by taking the ratio of two consecutive terms of the Fibonacci Sequence we get the ratio called the “ Golden Ratio “. Various search algorithms in computer technology use the Fibonacci sequence, etc.Various famous painting such as “Mona-Lisa” by Da-Vinci is based on the Fibonacci sequence.Fibonacci sequence is used in designing Automobiles.Fibonacci Sequence is used to design various buildings and to finalize their architecture.Some of the things created by humans by taking inspiration from the Fibonacci sequence are, Humans have taken inspiration from these examples and have applied the knowledge in creating various things that we observed in our daily life. ![]() In real-life we have encountered various examples that are based on the Fibonacci Sequence. Observing the formula we can see that, the first term of the sequence is F 0, not F 1 thus, the n term of the Fibonacci Sequence is F n-1 and the (n+1)th term of the Fibonacci Sequence is F n term. Thus, using the above-discussed formula we can easily find all the terms of the Fibonacci Sequence. ![]() Thus, the third term in the Fibonacci Sequence is 1, and similarly, the next terms of the sequence can also be found as, Using this formula we can easily find the various terms of the Fibonacci Sequence suppose we have to find the 3rd term of the Fibonacci Sequence then we would require the 2nd and the 1st term according to the given formula, then the 3rd term is calculated as, The nth term of the Fibonacci Sequence is represented as F n and the formula for the same is, Fibonacci Sequence Formulaįibonacci sequence formula is a formula that is used to find the nth term of the Fibonacci Sequence when its first and second term is given. Studying the Fibonacci Sequence or the Fibonacci Spiral it is evident that this sequence is very useful in studying various patterns in nature and this helps to easily understand the working of nature, (which is a complete mystery to humans). Thus, we see that for the larger term of the Fibonacci sequence, the ratio of two consecutive terms forms the Golden Ratio. Let us now calculate the ratio of every two successive terms of the Fibonacci sequence and see the result. The Fibonacci Spiral is shown in the image added below,Īfter studying the Fibonacci spiral we can say that every two consecutive terms of the Fibonacci sequence represent the length and breadth of a rectangle. Each quarter-circle fits perfectly within the next square in the sequence, creating a spiral pattern that expands outward infinitely. The side of the next square is the sum of the two previous squares, and so on. We start the construction of the spiral with a small square, followed by a larger square that is adjacent to the first square. Fibonacci SpiralĪ geometrical pattern derived from Fibonacci Sequence is called the Fibonacci pattern, this pattern is created by drawing a series of connected quarter-circles inside a set of squares that have their side according to the Fibonacci sequence. The first 20 terms of the Fibonacci sequence are represented in the table below,īy closely observing the table we can say that F n = F n-1 + F n-2 for every n > 1. ![]() Then the third term F 3 = F 2 + F 1 = 1 + 0 = 1 and so on.
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