This Fibonacci calculator can help you to find any n(th) term within the Fibonacci numbers/sequence and then the sum of the sequence by using the golden ratio formula. You can learn more on this topic below the tool.

## How does this Fibonacci calculator work?

In mathematics, the Fibonacci sequence is defined as a number sequence having the particularity that the first two numbers are 0 and 1, and that each subsequent number is obtained by the sum of the previous two terms. Fibonacci formula:

f_{0} = 0 f_{1} = 1

f_{n} = f_{n-1} + f_{n-2}

To figure out the n^{th }term (x_{n}) in the sequence this Fibonacci calculator uses the golden ratio number, as explained below:

Φ (phi) = (1+√5)/2 = 1.6180339887

x_{n}=[1.6180339887^{n} – (-0.6180339887)^{n}]/√5

To determine the sum of all numbers until the ^{nth }term within the Fibonacci sequence first you should calculate the (n+2)^{th }term in the sequence and then subtract 1 from it:

Sum until the n^{th term }= f_{n+2} - 1

## Example of a calculation

Assuming we want to figure out the 25^{th} number in the Fibonacci sequence and then find out the sum of all numbers until 25^{th} term:

25^{th} = 75025

Sum until the 25^{th} term = 196417

This is because the 27^{th} (25+ 2)^{th }number is 196418, and if we subtract 1 from it we will get the right value 196417.