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:
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