Math Problem Statement

What is the 60th number of Fibonacci sequence?

Solution

To find the 60th number of the Fibonacci sequence, we use the recurrence relation:

F(n)=F(n1)+F(n2)F(n) = F(n-1) + F(n-2)

with initial conditions:

F(0)=0,F(1)=1F(0) = 0, \quad F(1) = 1

The Fibonacci sequence starts as follows: 0,1,1,2,3,5,8,13,21,34,55,89,0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \dots

You can compute the 60th Fibonacci number either by writing out all terms or using an efficient algorithm. By calculating or using a precomputed list of Fibonacci numbers, we find:

F(60)=1548008755920F(60) = 1548008755920

So, the 60th Fibonacci number is 1,548,008,755,920.

Let me know if you would like more details on the calculation or further questions!

Related questions:

  1. How do you derive the Fibonacci sequence using a recursive algorithm?
  2. What is the relationship between Fibonacci numbers and the golden ratio?
  3. How can Fibonacci numbers be used in real-world applications?
  4. What is the time complexity of calculating Fibonacci numbers using recursion versus iteration?
  5. How can Fibonacci numbers be computed efficiently using matrix exponentiation?

Tip: The Fibonacci sequence grows exponentially, so even the 60th term is a large number, highlighting the rapid growth of the series!

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Math Problem Analysis

Mathematical Concepts

Recurrence Relations
Fibonacci Sequence
Exponential Growth

Formulas

F(n) = F(n-1) + F(n-2)
Initial conditions: F(0) = 0, F(1) = 1

Theorems

Recurrence Relation Principle

Suitable Grade Level

Grades 9-12