Nth Term of Fibonaccci Sequence using Golden Ratio Calculator

✖Value of N of Fibonacci Sequence is the position or index of a term in the Fibonacci Sequence.ⓘ Value of N of Fibonacci Sequence [n_Fib]

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✖Nth Term of Fibonacci Sequence is the term corresponding to the index or position n from the beginning of the given Fibonacci Sequence.ⓘ Nth Term of Fibonaccci Sequence using Golden Ratio [F_n]

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Formula

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Nth Term of Fibonaccci Sequence using Golden Ratio

Formula

`"F"_{"n"} = ("[phi]"^("n"_{"Fib"})-(1-"[phi]")^("n"_{"Fib"}))/sqrt(5)`

Example

`"21"=("[phi]"^("8")-(1-"[phi]")^("8"))/sqrt(5)`

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Nth Term of Fibonaccci Sequence using Golden Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5)
F_n = ([phi]^(n_Fib)-(1-[phi])^(n_Fib))/sqrt(5)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Nth Term of Fibonacci Sequence - Nth Term of Fibonacci Sequence is the term corresponding to the index or position n from the beginning of the given Fibonacci Sequence.
Value of N of Fibonacci Sequence - Value of N of Fibonacci Sequence is the position or index of a term in the Fibonacci Sequence.

STEP 1: Convert Input(s) to Base Unit

Value of N of Fibonacci Sequence: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_n = ([phi]^(n_Fib)-(1-[phi])^(n_Fib))/sqrt(5) --> ([phi]^(8)-(1-[phi])^(8))/sqrt(5)

Evaluating ... ...

F_n = 21

STEP 3: Convert Result to Output's Unit

21 --> No Conversion Required

FINAL ANSWER

21 <-- Nth Term of Fibonacci Sequence

(Calculation completed in 00.004 seconds)

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< 5 Fibonacci Sequence Calculators

Nth Term of Fibonaccci Sequence using Golden Ratio

Go Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5)

Nth Term of Fibonaccci Sequence

Go Nth Term of Fibonacci Sequence = (N-1)th Term of Fibonacci Sequence+(N-2)th Term of Fibonacci Sequence

Sum of First N Even Index Fibonacci Numbers

Go Sum of First N Even Index Fibonacci Numbers = (2N+1)th Term of Fibonacci Sequence-1

Sum of First N Odd Index Fibonacci Numbers

Go Sum of First N Odd Index Fibonacci Numbers = 1*2Nth Term of Fibonacci Sequence

Sum of First N Fibonacci Numbers

Go Sum of First N Fibonacci Numbers = (N+2)th Term of Fibonacci Sequence-1

Nth Term of Fibonaccci Sequence using Golden Ratio Formula

Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5)
F_n = ([phi]^(n_Fib)-(1-[phi])^(n_Fib))/sqrt(5)

What is Fibonacci Sequence?

The Fibonacci sequence is a type series where each number is the sum of the two that precede it. It starts from 0 and 1 usually. The Fibonacci sequence is given by 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. The numbers in the Fibonacci sequence are also called Fibonacci numbers. In Maths, the sequence is defined as an ordered list of numbers that follow a specific pattern. The numbers present in the sequence are called the terms. The different types of sequences are arithmetic sequence, geometric sequence, harmonic sequence and Fibonacci sequence.

How to Calculate Nth Term of Fibonaccci Sequence using Golden Ratio?

Nth Term of Fibonaccci Sequence using Golden Ratio calculator uses Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5) to calculate the Nth Term of Fibonacci Sequence, The Nth Term of Fibonaccci Sequence using Golden Ratio formula is defined as the term corresponding to the index or position n from the beginning of the given Fibonacci Sequence, calculated using the golden ratio. Nth Term of Fibonacci Sequence is denoted by F_n symbol.

How to calculate Nth Term of Fibonaccci Sequence using Golden Ratio using this online calculator? To use this online calculator for Nth Term of Fibonaccci Sequence using Golden Ratio, enter Value of N of Fibonacci Sequence (n_Fib) and hit the calculate button. Here is how the Nth Term of Fibonaccci Sequence using Golden Ratio calculation can be explained with given input values -> 21 = ([phi]^(8)-(1-[phi])^(8))/sqrt(5).

FAQ

What is Nth Term of Fibonaccci Sequence using Golden Ratio?

The Nth Term of Fibonaccci Sequence using Golden Ratio formula is defined as the term corresponding to the index or position n from the beginning of the given Fibonacci Sequence, calculated using the golden ratio and is represented as F_n = ([phi]^(n_Fib)-(1-[phi])^(n_Fib))/sqrt(5) or Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5). Value of N of Fibonacci Sequence is the position or index of a term in the Fibonacci Sequence.

How to calculate Nth Term of Fibonaccci Sequence using Golden Ratio?

The Nth Term of Fibonaccci Sequence using Golden Ratio formula is defined as the term corresponding to the index or position n from the beginning of the given Fibonacci Sequence, calculated using the golden ratio is calculated using Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5). To calculate Nth Term of Fibonaccci Sequence using Golden Ratio, you need Value of N of Fibonacci Sequence (n_Fib). With our tool, you need to enter the respective value for Value of N of Fibonacci Sequence and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Nth Term of Fibonacci Sequence?

In this formula, Nth Term of Fibonacci Sequence uses Value of N of Fibonacci Sequence. We can use 1 other way(s) to calculate the same, which is/are as follows -

Nth Term of Fibonacci Sequence = (N-1)th Term of Fibonacci Sequence+(N-2)th Term of Fibonacci Sequence

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