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JEE Main 2026 Preparation: Question Papers, Solutions, Mock Tests & Strategy Unacademy » JEE Study Material » Mathematics » Fibonacci Numbers Lines

Fibonacci Numbers Lines

The Fibonacci numbers are the numbers that can be shown in the progression of 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55….The next term of the Fibonacci sequence can be found by adding the two terms before it.

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Fibonacci numbers are said to be of great importance in the fields of biology and physics. It is because these numbers are very helpful in the observation of objects and the phenomenon that is associated with those objects. The branching of data or information acts as a suitable example of the Fibonacci series, and it also reflects the great role that these numbers play in our lives. It is possible to find the Fibonacci numbers to whatever term we desire by using simple formulas. 

Fibonacci sequence

Fibonacci is a progression or sequence in which the next term for the sequence can be given by adding up the two terms that were used before it. The same process needs to be carried out to gain more terms of that sequence. 

Fibonacci is a sequence made up of a set of integers that starts with zero and is followed by one, and then by another one, and then it just keeps going on. After the second one, the next term of that sequence can be given by taking the sum of the last two terms of the term that you are trying to find right now. 

This sequence made up of integers can go on for as far as infinity. It can also be noticed in many prospects that the Fibonacci series is said to start from one and not zero. However, that much of a difference can be said only to be irrelevant. The same principle will be used to find the next term for the series as before. But, the series is much preferred if it is starting from the integer 0. 

Using the last two terms of a Fibonacci series, you can always find the next terms of that sequence. Hence, it can be said to be quite efficient.

Fibonacci meaning

The term Fibonacci has a set of predefined integers given in the form of 0 and 1.  After putting these two numbers in a sequence it is possible to define every number that is to come after these two. Seeing as the next term will be the sum of the two terms preceding it. Hence, by using this simple method we can find as high of a Fibonacci term as we want. All we will be needing to do is to find the two Fibonacci terms that are preceding the one that we are searching for. 

This number is referred to as an indicator of the financial stability of the market. It is said that by following this sequence word to word, it is possible to conclude if the market will rise, fall or will maintain its grounds. This gives us clues about what the market will behave like in the future. It can be noted in a Fibonacci sequence that the term next to the one that you will be writing right now will be nearly 1.618 greater than the current one. This relation does not stand true for all the terms in the sequence, it is meant only for the terms that come later on.  

Fibonacci series formula

The Fibonacci terms in the Fibonacci sequence can be found using the mathematical operations that are related to the sequence. However, it is to be noted that the Fibonacci sequence starts from 0. Hence, zero will be the first term of the series and will be represented by F0.

The terms of a Fibonacci series can be given in the following way:

F0 = 0

F1 = 1

F2 = 1

These are the values for the Fibonacci series that always remain constant in it. For a Fibonacci series to start, there must be these terms present in that sequence. However, the terms after that can be given by utilising the following formula:

Fn = Fn – 1 + Fn – 2

Fn is the term in the sequence that we need to find; Fn – 1 is the term that is before what we are trying to find; Fn – 2 is the term before even that term. 

Conclusion

The Fibonacci sequence in itself is a suitable example of the golden ratio or the ratio of 1 to 1.618. It can be said so because the existence of this ratio is observed in the entire world of science and mathematics quite fairly. The use of Fibonacci terms does not limit itself only to mathematics, this sequence is applicable in the field of architecture and the web development industry. It helps in increasing the efficiency of the data that is available to us.

faq

Frequently asked questions

Get answers to the most common queries related to the JEE Examination Preparation.

How can you possibly find the 18th term of the Fibonacci sequence?

Ans. To find the 18th term of the Fibonacci sequence, you will need to find the 16th and 17th terms...Read full

What is the common ground on which both the Fibonacci sequence starting from 0 and starting from 1 can be based?

Ans. Both of these sequences follow the same way to find the next term of the sequence. You will need to add...Read full

What is the ratio that is fairly seen in the higher terms of the Fibonacci series?

Ans. The ratio is referred to as the golden ratio and is given by 1: 1.618.

What is the 8th term of the Fibonacci sequence?

Ans. The 8th term of the Fibonacci sequence is 13.

What is the relation between the two consecutive terms of a Fibonacci sequence?

Ans. The term before the higher number term will be 0.618 times the later one. 

Ans. To find the 18th term of the Fibonacci sequence, you will need to find the 16th and 17th terms of that sequence, and add up both of those. The outcome will be the 18th term of the sequence.

Ans. Both of these sequences follow the same way to find the next term of the sequence. You will need to add the previous two terms of the sequence to get the next term of the progression.

Ans. The ratio is referred to as the golden ratio and is given by 1: 1.618.

Ans. The 8th term of the Fibonacci sequence is 13.

Ans. The term before the higher number term will be 0.618 times the later one. 

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