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.

The nth number to obtain:*

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:

f0 = 0     f1 = 1
fn = fn-1 + fn-2

To figure out the nth term (xn) in the sequence this Fibonacci calculator uses the golden ratio number, as explained below:

Φ (phi) = (1+√5)/2 = 1.6180339887

xn=[1.6180339887n – (-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 nth term = fn+2 - 1

Example of a calculation

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

25th = 75025

Sum until the 25th term = 196417

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

14 Jun, 2015