Math Problem Statement

Find Fibonacci(8)

Solution

It looks like the image asks to "Find Fibonacci(8)". The Fibonacci sequence is defined as follows:

F(0)=0,F(1)=1F(0) = 0, \quad F(1) = 1 F(n)=F(n1)+F(n2)forn2F(n) = F(n-1) + F(n-2) \quad \text{for} \, n \geq 2

Now, let's calculate Fibonacci(8):

F(2)=F(1)+F(0)=1+0=1F(2) = F(1) + F(0) = 1 + 0 = 1 F(3)=F(2)+F(1)=1+1=2F(3) = F(2) + F(1) = 1 + 1 = 2 F(4)=F(3)+F(2)=2+1=3F(4) = F(3) + F(2) = 2 + 1 = 3 F(5)=F(4)+F(3)=3+2=5F(5) = F(4) + F(3) = 3 + 2 = 5 F(6)=F(5)+F(4)=5+3=8F(6) = F(5) + F(4) = 5 + 3 = 8 F(7)=F(6)+F(5)=8+5=13F(7) = F(6) + F(5) = 8 + 5 = 13 F(8)=F(7)+F(6)=13+8=21F(8) = F(7) + F(6) = 13 + 8 = 21

Thus, Fibonacci(8) is 21.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:

  1. How is the Fibonacci sequence related to the golden ratio?
  2. Can you derive a formula for Fibonacci numbers using recursion?
  3. What are some real-world applications of Fibonacci numbers?
  4. How can you compute large Fibonacci numbers efficiently?
  5. What is the closed-form expression for Fibonacci numbers (Binet's formula)?

Tip: Fibonacci numbers grow exponentially, but you can approximate large values using the golden ratio to simplify calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Sequences
Fibonacci Sequence

Formulas

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

Theorems

Fibonacci Sequence Definition

Suitable Grade Level

Grades 6-8