Fibonacci Sequence Examples
We have solved some questions on Fibonacci Sequence to help you consolidate your concepts.
Example 1: Find the 7th term of the Fibonacci sequence if the 5th and 6th terms are 3 and 5 respectively.
Solution:
Using the Fibonacci sequence recursive formula,
7th term = 6th term + 5th term
F6 = 3 + 5 = 8
Thus, the 7th term of the Fibonacci Sequence is F6 = 8
Example 2: If F9 in the Fibonacci sequence is 34. Find the next term(F10)
Solution:
We know that,
Fn = Fn-1 × Φ
where, Φ is golden ration and its value is 1.618034
F9 = 34 × Φ
= 34 × (1.618034)
= 55.0131
= 55
Thus, the F9 term in the Fibonacci Sequence is 55.
Example 3: Find the 10th term of the Fibonacci sequence if the 8th and 9th terms are 13 and 21 respectively.
Solution:
Using the Fibonacci sequence recursive formula,
10th term = 9th term + 8th term
F9 = 13 + 21 = 34
Thus, the 10th term of the Fibonacci Sequence is F9 = 34
Example 4: If F12 in the Fibonacci sequence is 144. Find the next term(F13)
Solution:
We know that,
Fn = Fn-1 × Φ
where, Φ is golden ration and its value is 1.618034
F13 = 144 × Φ
= 144 × (1.618034)
= 232.996
= 233
Thus, the F13 term in the Fibonacci Sequence is 233.
Must Read
Fibonacci Sequence: Definition, Formula, List and Examples
Fibonacci sequence is a series of numbers where each number is the sum of the two numbers that come before it. The numbers in the Fibonacci sequence are known as Fibonacci numbers and are usually represented by the symbol Fₙ. Fibonacci sequence numbers start with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
Fibonacci Sequence
Table of Content
- Fibonacci Sequence
- Fibonacci Sequence Formula
- Fibonacci Spiral
- Golden Ratio to find Fibonacci Sequence
- Golden Ratio Formula
- Fibonacci Series in Pascal’s Triangle
- Fibonacci Sequence Properties
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence
- Fibonacci Sequence – FAQs
There are various applications of Fibonacci sequence in real life, such as in the growth of trees. As the tree grows, the trunk grows and spirals outward. The branches also follow the Fibonacci sequence, starting with one trunk that splits into two, then one of those branches splits into two, and so on.
Let’s learn about Fibonacci Sequence in detail, including Fibonacci sequence formula, properties, and examples.