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Nth Term of Fibonaccci Sequence using Golden Ratio Formula

GoNth Term of Fibonaccci Sequence Formula

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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. Check FAQs

F n = \frac{{[phi]}^{n Fib} - {(1 - [phi])}^{n Fib}}{\sqrt{5}}

F_n - Nth Term of Fibonacci Sequence?n_Fib - Value of N of Fibonacci Sequence?[phi] - Golden ratio?[phi] - Golden ratio?

Nth Term of Fibonaccci Sequence using Golden Ratio Example

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Here is how the Nth Term of Fibonaccci Sequence using Golden Ratio equation looks like with Values.

Here is how the Nth Term of Fibonaccci Sequence using Golden Ratio equation looks like with Units.

Here is how the Nth Term of Fibonaccci Sequence using Golden Ratio equation looks like.

21 = \frac{{1.618}^{8} - {(1 - 1.618)}^{8}}{\sqrt{5}}

21 = \frac{{1.618}^{8} - {(1 - 1.618)}^{8}}{\sqrt{5}}

21 = \frac{{1.618}^{8} - {(1 - 1.618)}^{8}}{\sqrt{5}}

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Nth Term of Fibonaccci Sequence using Golden Ratio Solution

Follow our step by step solution on how to calculate Nth Term of Fibonaccci Sequence using Golden Ratio?

FIRST Step Consider the formula

F n = \frac{{[phi]}^{n Fib} - {(1 - [phi])}^{n Fib}}{\sqrt{5}}

Next Step Substitute values of Variables

∴

F n = \frac{{[phi]}^{8} - {(1 - [phi])}^{8}}{\sqrt{5}}

Next Step Substitute values of Constants

∴

F n = \frac{{1.618}^{8} - {(1 - 1.618)}^{8}}{\sqrt{5}}

Next Step Prepare to Evaluate

∴

F n = \frac{{1.618}^{8} - {(1 - 1.618)}^{8}}{\sqrt{5}}

LAST Step Evaluate

∴

F n = 21

Nth Term of Fibonaccci Sequence using Golden Ratio Formula Elements

Variables

Constants

Functions

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.

Symbol: F_n

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Nth Term of 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.

Symbol: n_Fib

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of N of Fibonacci Sequence

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

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.

Syntax: sqrt(Number)

Other Formulas to find Nth Term of Fibonacci Sequence

Go Nth Term of Fibonaccci Sequence

F n = F n-1 + F n-2

Other formulas in Fibonacci Sequence category

Go Sum of First N Fibonacci Numbers

S n(Fib) = F n+2 - 1

Go Sum of First N Even Index Fibonacci Numbers

S n(Fib)Even = F 2n+1 - 1

Go Sum of First N Odd Index Fibonacci Numbers

S n(Fib)Odd = 1 \cdot F 2n

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

Nth Term of Fibonaccci Sequence using Golden Ratio evaluator uses Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5) to evaluate 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 evaluate Nth Term of Fibonaccci Sequence using Golden Ratio using this online evaluator? To use this online evaluator for Nth Term of Fibonaccci Sequence using Golden Ratio, enter Value of N of Fibonacci Sequence (n_Fib) and hit the calculate button.

FAQs on Nth Term of Fibonaccci Sequence using Golden Ratio

What is the formula to find Nth Term of Fibonaccci Sequence using Golden Ratio?

The formula of Nth Term of Fibonaccci Sequence using Golden Ratio is expressed as Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5). Here is an example- 21 = ([phi]^(8)-(1-[phi])^(8))/sqrt(5).

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

With Value of N of Fibonacci Sequence (n_Fib) we can find Nth Term of Fibonaccci Sequence using Golden Ratio using the formula - Nth Term of Fibonacci Sequence = ([phi]^(Value of N of Fibonacci Sequence)-(1-[phi])^(Value of N of Fibonacci Sequence))/sqrt(5). This formula also uses Golden ratio, Golden ratio constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Nth Term of Fibonacci Sequence?

Here are the different ways to Calculate Nth Term of Fibonacci Sequence-

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

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