Fibonacci Sequence Formula
The Fibonacci sequence was first found by an Italian named Leonardo Pisano Bigollo. Fibonacci numbers are a sequence of whole numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... This infinite sequence is called the Fibonacci sequence. Observe that, the first number in a Fibonacci sequence is always 0. The Fibonacci sequence formula is useful to find any of the terms of the Fibonacci sequence. Fibonacci sequence is represented as the spiral shown below.
The Fibonacci formula is used for calculating the numbers in the Fibonacci sequence. Let us learn the Fibonacci formula with its derivation and a few solved examples.
What is the Fibonacci Formula?
The Fibonacci formula, if explained in simple terms, says that every number in the Fibonacci sequence is the sum of two numbers preceding it in the sequence. Thus, the Fibonacci formula is given as follows.
F_{n} = F_{(n1)} + F_{(n2)} , where n > 1
The following table shows a few Fibonacci numbers using the Fibonacci formula.
You can use the fibonacci calculator that helps to calculate the Fibonacci Sequence. Look at a few solved examples to understand the Fibonacci formula better.
Solved Examples Using Fibonacci Formula

Example 1: Find the 12^{th} term of the Fibonacci sequence if the 10^{th} and 11^{th} terms are 34 and 55 respectively.
Solution:
Using Fibonacci formula, we can say that the 12^{th} term is the sum of 10^{th} term and 11^{th} term.
12^{th} term = 10^{th} term + 11^{th} term
= 34 + 55
= 89
Answer: The 12^{th} term of the Fibonacci sequence is 89.

Example 2: Find the sum of first 10 terms of the Fibonacci sequence.
Solution:
By Fibonacci formula, the first 10 Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Sum = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 = 88
Answer: The sum of first 10 terms of the Fibonacci sequence is 88.