What is the fibonacci sequence – In mathematics, the Fibonacci sequence is a set in which each number is the sum of the previous two. The numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly referred to as Fn. The sequence generally starts with 0 and 1, although some authors have started with 1 and 1 or sometimes (like Fibonacci) with 1 and 2. some starts with 0 and 1, the sequence start with 0, 1, 1, 2 , 3, 5, 8, 13, 21, 34, 55, 88, 144…

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## About Fibonacci sequence

It is a set of integers starting with zero, followed by one, then another, and then a series of continuously growing numbers. The fibonacci sequence follows the instruction that each number is equal to the sum of the two previous numbers.

The Fibonacci sequence starts with the following 14 numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 144, 233…

Every number begins with the third, follows a fixed formula. For example, the 7th number, 8, is led by 3 and 5, which add up to 8.

In theory, the sequence could continue ad infinitum, using the same formula for each new number. Some author show the Fibonacci sequence starting at one instead of zero, but this is quite uncommon.

## Why is Fibonacci so important?

The Fibonacci sequence is important for many reasons. In nature, the numbers and ratios in the sequence can be found in the patterns of petals of flowers, the whorls of a pine cone, and the leaves on stems. As the sequence continues, the ratios of the terms approach a number known as the golden ratio.

## What is golden ratio in Fibonacci?

The golden ratio, also called the golden number, golden ratio or divine ratio, is a ratio between two numbers that is approximately equal to 1.618. Commonly written as the Greek letter phi, it is strongly related with the Fibonacci system, a sequence of numbers in which each number is added to the last.

## Calculating the Fibonacci sequence

The Fibonacci sequence can calculated mathematically. In this method, each number in the sequence is considered a term, represented by the expression Fn. n represents the position of the number in the sequence starting from zero. For example, the sixth term is F5 and the seventh is F6.

Using this number, the Fibonacci sequence can be described by the following three equations:

F0 = 0 (Applies to first digit only)

F1 = 1 (only applies to second integer)

Fn = Fn-1 + Fn-2 (applies to all integers)

The first two equations basically state that the first term is equal to 0 and the second term is equal to 1. The third equation is a recursive formula, meaning that each sequence number is defined using the previous numbers. For example, to limit the fifth number (F4), the terms F2 and F3 must be defined beforehand. These two numbers, in turn, require limiting the numbers preceding them. The numbers continuously complement each other through the sequence.

### Formula for Fibonacci sequence

You can try the formula yourself, using the table to find the sequence numbers that precede the value of the target term. For example, the following calculation gives the Fibonacci number for the term in the tenths position F9.

F9 = F9-1 + F9-2 = F8 + F7 = 21 + 14 = 34

The contest with the recursion formula is that it always relies on knowing the earlier Fibonacci numbers to calculate a specific number in the sequence. For example, you cannot calculate the value of term 100 without knowing terms 98 and 99, which requires that you know all the terms before them. However, other equations can be used, such as the Binet formula, a closed-form expression for finding the Fibonacci sequence numbers. Another option is to program the recursive formula logic into application code such as Python, Java, or PHP and then let the processor do the work for you.

## How to Use the Fibonacci Sequence

The Fibonacci sequence can useful to finance using four techniques: retracements, arcs, fans, and time zones.

Fibonacci retracements require two selected price points on the chart, usually a high and a low. Once two points are chosen, Fibonacci numbers and lines are drawn in percentages of that movement. If a stock rises from $15 to $21, the 23.6% level is $18.83, or $20 – ($5 x 0.236) = $18.82. The 50% level is $17.50, or $15 – ($5 x 0.5) = $17.50.

Fibonacci retracements are the most usual form of technical analysis based on the Fibonacci sequences. During a trend, Fibonacci retracements can use to determine how deep the retracement may be. Traders look for Fibonacci ratios between 23.6% and 78.6% during these times. If the price stops near one of the Fibonacci levels and then starts to retrace in the way of the trend, a trader can trade in the direction of the trend.

Arcs, fans, and time zones are almost same concepts but applied differently to charts. Each one shows potential areas of support based on Fibonacci numbers involved in prior price moves. These helpful or resistance levels can be use to forecast where prices may fall or rise.

## How Can the Fibonacci Sequence Affect Trading Performance?

Humans tend to identify patterns, and dealers easily equate patterns in charts through the Fibonacci sequence. It’s unproven that Fibonacci numbers relate to fundamental market forces. However, by design, markets react to their players’ beliefs. Consequently, if stakeholders buy or sell because of the Fibonacci analysis, they tend to create a self-fulfilling prophecy that affects the market trends.

## conclusion

A Fibonacci sequence is a series of continuously increasing numbers where each is equal to the sum of the previous two numbers. Many objects in nature have dimensional properties that follow to the golden ratio of 1.618, a derivative of the Fibonacci sequences. When applied to finance and trading, investors use the Fibonacci sequences through four techniques: retracements, arcs, fans, and time zones.