This Fibonacci calculator is a convenient tool you can use to solve for the arbitrary terms of the Fibonacci sequence. With this calculator, you don’t have to perform the calculations by hand using the Fibonacci formula. This Fibonacci sequence calculator is so efficient that it can provide you with the first 200 terms of the sequence doing all of the work for you.
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How to use the Fibonacci calculator?
This Fibonacci calculator is also known as a Fibonacci sequence calculator, a Fibonacci number calculator or a Fib calculator. It’s an easy to use online tool which performs the calculations for you. Here are the steps for you to follow for this online tool:
- You only need one value for this calculator. Enter the value of n.
- After this, the Fibonacci number calculator automatically generates for you the value of the Results along with the Sequence Terms.
Why is the Fibonacci sequence so important?
Why would you need to use a Fib calculator in the first place? The Fibonacci sequence reflects patterns of growth spirals found in nature. This doesn’t make the Fibonacci sequence important as such. This just shows how it occurs naturally like in the different patterns found in nature.
At the very heart of the evolution of living things, there is a special underlying geometry. This is the important part because a lot of people aren’t aware of this. Even Darwin didn’t mention this fact in his Theory of Natural Selection. Once you understand this underlying geometry, you’ll start seeing the importance of the Fibonacci sequence.
The importance of the Fibonacci sequence depends on you and your own interests. The idea behind this sequence is very simple making it easy for most people to understand the idea. This is another thing that makes the Fibonacci sequence so special. When you think about it, the name is quite catchy too.
The Fibonacci sequence has a sort of mystical quality to it. Although it was first discovered back in the Middle Ages, people have discovered and rediscovered the numbers and the sequence in the most unexpected of places. It also has a number of important applications which we will discuss more later.
How do you find the Fibonacci sequence?
Before you can understand the Fibonacci calculator, you must first understand the Fibonacci sequence. This refers to a sequence of numbers which follow a special rule. Each number in the sequence is the sum of the two terms before it. Therefore, you can compute for this sequence using the Fibonacci formula:
xₐ = xₐ₋₁ + xₐ₋₂
Typically, the first two terms of the Fibonacci sequence are equal to x₀ = 0 and x₁ = 1. Then again, you may also use x₁ = 1 and x₂ = 1 as the first two terms of your sequence. The Fibonacci sequence isn’t like an arithmetic sequence where you should know at least two consecutive terms so you can solve for the next numbers.
Another thing that makes this sequence special is that it applies to negative terms too. For instance, you can solve x₋₁ to be equal to 1. For this, the first ten terms of the Fibonacci sequence will be 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …
The good news is that computing for the nth term of this sequence doesn’t mean that you have to calculate all of the terms before it. Instead, you can use a simple formula for you to solve for an arbitrary term of the sequence. The formula is:
xₐ = (φⁿ – ψⁿ) / √5
where:
xₐ refers to the nth term of the sequence,
φ refers to the golden ratio which is equal to (1 + √5)/2, or 1.618…)
This Fibonacci calculator makes use of this formula to generate arbitrary terms in an instant. For a Fibonacci sequence, you can also find arbitrary terms using different starters. For this, there is a generalized formula to use for solving the nth term. The formula to use is:
xₐ = aφⁿ + bψⁿ
where:
a is equal to (x₁ – x₀ψ) / √5
b is equal to (φx₀ – x₁) / √5
x₀ refers to the first term of the sequence
x₁ refers to the second term of the sequence.
What is the Fibonacci sequence used for?
There is an excellent example which shows the power of math in Fibonacci numbers. The Fibonacci sequence was first discovered by Leonardo Fibonacci, a mathematician from Italy back in the 13th century. This is a special sequence because it has a number of noteworthy properties.
Firstly, the sum of any two consecutive terms is equal to the next number. After the first four digits, the ratio of any term to the next highest number approaches the value 0.618. Then the ratio of alternate terms approaches 0.382. Although several features of the Fibonacci sequence occur throughout nature, these aren’t the only applications.
Secondly, investors have used the power of the Fibonacci sequence for the prediction of stock prices. The most well-known investment system that’s Fibonacci-based is the Elliot Wave Theory. However, since stock markets are very volatile and complex, you may also consider these other applications of the Fibonacci sequence in terms of retracement levels:
- Support and resistance levels
One weakness of retracement is that you can only measure them by looking backward. But such reviews offer patterns which are quite impressive. When you apply the Fibonacci sequence to these stock market events, you would start seeing a downside price target. - Changes in trends
Most of the time, prices tend to consolidate when they’re nearing retracement levels. No matter what the potential of a trend is, when it approaches retracements, this will end up slowing down the pace. - Price targets
This is where you can apply the use of the Fibonacci sequence the most. When prices bottom out and start rallying, the retracement level becomes an obvious price target. When shares reach a target price at a rapid pace, this shouldn’t come as a surprise to anyone.
